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Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Intermediate Algebra

In the following exercises, solve by using the Quadratic Formula. 124. 5b2+2b4=0 In the following exercises, solve by using the Quadratic Formula. 125. x2+8x4=0 In the following exercises, solve by using the Quadratic Formula. 126. y2+4y4=0 In the following exercises, solve by using the Quadratic Formula. 127. 3y2+5y2=0 In the following exercises, solve by using the Quadratic Formula. 128. 6x2+2x20=0 In the following exercises, solve by using the Quadratic Formula. 129. 2x2+3x+3=0 In the following exercises, solve by using the Quadratic Formula. 130. 2x2x+1=0 In the following exercises, solve by using the Quadratic Formula. 131. 8x26x+2=0 In the following exercises, solve by using the Quadratic Formula. 132. 8x24x+1=0 In the following exercises, solve by using the Quadratic Formula. 133. (v+1)(v5)4=0 In the following exercises, solve by using the Quadratic Formula. 134. (x+1)(x3)=2 In the following exercises, solve by using the Quadratic Formula. 135. (y+4)(y7)=18 In the following exercises, solve by using the Quadratic Formula. 136. (x+2)(x+6)=21 In the following exercises, solve by using the Quadratic Formula. 137. 13m2+112m=14 In the following exercises, solve by using the Quadratic Formula. 138. 13n2+n=12 In the following exercises, solve by using the Quadratic Formula. 139. 34b2+12b=38 In the following exercises, solve by using the Quadratic Formula. 140. 19c2+23c=3 In the following exercises, solve by using the Quadratic Formula. 141. 16c2+24c+9=0 In the following exercises, solve by using the Quadratic Formula. 142. 25d260d+36=0 In the following exercises, solve by using the Quadratic Formula. 143. 25q2+30q+9=0 In the following exercises, solve by using the Quadratic Formula. 144. 16y2+8y+1=0 In the following exercises, determine the number of real solutions for each quadratic equation. 145. (a) 4x25x+16=0 (b) 36y2+36y+9=0 (c) 6m2+3m5=0 In the following exercises, determine the number of real solutions for each quadratic equation. 146. (a) 9v215v+25=0 (b) 100w2+60w+9=0 (c) 5c2+7c10=0 In the following exercises, determine the number of real solutions for each quadratic equation. 147. (a) r2+12r+36=0 (b) 8t211t+5=0 (c) 3v25v1=0 In the following exercises, determine the number of real solutions for each quadratic equation. 148. (a) 25p2+10p+1=0 (b) 7q23q6=0 (c) 7y2+2y+8=0 In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve. 149. (a) x25x24=0 (b) (y+5)2=12 (c) 14m2+3m=11 In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve. 150. (a) (8v+3)2=81 (b) w29w22=0 (c) 4n210=6 In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve. 151. (a) 6a2+14=20 (b) (x14)2=516 (c) y22y=8 In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve. 152. (a) 8b2+15b=4 (b) 59v223v=1 (c) (w+43)2=29 Solve the equation x2+10x=120 (a) by completing the square (b) using the Quadratic Formula (c) Which method do you prefer? Why?Solve the equation 12y2+23y=24 (a) by completing the square (b) using the Quadratic Formula (c) Which method do you prefer? Why?Solve: x46x2+8=0.Solve: x 4 11 x 2 +28=0.Solve: (x5)2+6(x5)+8=0.Solve: (y4)2+8(y4)+15=0.Solve: x7x+12=0.Solve: x6x+8=0.Solve: x235x1314=0.Solve: x12+8x14+15=0.Solve: 8x210x1+3=0.Solve: 6x223x1+20=0.In the following exercises, solve. 155. x47x2+12=0 In the following exercises, solve. 156. x49x2+18=0 In the following exercises, solve. 157. x413x230=0 In the following exercises, solve. 158. x4+5x236=0 In the following exercises, solve. 159. 2x45x2+3=0 In the following exercises, solve. 160. 4x45x2+1=0 In the following exercises, solve. 161. 2x47x2+3=0 In the following exercises, solve. 162. 3x414x2+8=0 In the following exercises, solve. 163. (x3)25(x3)36=0 In the following exercises, solve. 164. (x+2)23(x+2)54=0 In the following exercises, solve. 165. (3y+2)2+(3y+2)6=0 In the following exercises, solve. 166. (5y1)2+3(5y1)28=0 In the following exercises, solve. 167. (x2+1)25(x2+1)+4=0 In the following exercises, solve. 168. (x24)24(x24)+3=0 In the following exercises, solve. 169. 2(x25)25(x25)+2=0 In the following exercises, solve. 170. 2(x25)27(x25)+6=0 In the following exercises, solve. 171. xx20=0 In the following exercises, solve. 172. x8x+15=0 In the following exercises, solve. 173. x+6x16=0 In the following exercises, solve. 174. x+4x21=0 In the following exercises, solve. 175. 6x+x2=0 In the following exercises, solve. 176. 6x+x1=0 In the following exercises, solve. 177. 10x17x+3=0 In the following exercises, solve. 178. 12x+5x3=0 In the following exercises, solve. 179. x23+9x13+8=0 In the following exercises, solve. 180. x233x13=28 In the following exercises, solve. 181. x23+4x13=12 In the following exercises, solve. 182. x2311x13+30=0 In the following exercises, solve. 183. 6x23x13=12 In the following exercises, solve. 184. 3x2310x13=8 In the following exercises, solve. 185. 8x2343x13+15=0 In the following exercises, solve. 186. 20x2323x13+6=0 In the following exercises, solve. 187. x+8x12+7=0 In the following exercises, solve. 188. 2x7x12=15 In the following exercises, solve. 189. 6x2+13x1+5=0 In the following exercises, solve. 190. 15x226x1+8=0 In the following exercises, solve. 191. 8x22x13=0 In the following exercises, solve. 192. 15x24x14=0 In the following exercises, solve. 193. Explain how to recognize an equation in quadratic form.In the following exercises, solve. 194. Explain the procedure for solving an equation in quadratic form.The product of two consecutive odd is 99. Find the integers.The product of two consecutive even integers is 168. Find the integers.Find the base and height of a triangle whose base is four inches more than six times height and hasan area of 456 square inches.If a triangle that has an area of 110 square feet has a base that is two feet less than twice the height, what is the length of its base and height?The length of a 200 square foot rectangular vegetable garden is four feet less than twice the width. Find the length and width of the garden, to the nearest tenth of a foot.A rectangular tablecloth has an area of 80 square feet. The width is 5 feet shorter than the length and what are the length and width of the tablecloth to the nearest tenth of a foot.?The sun casts a shadow from a flag pole. The height of the flag pole is three times the length of its shadow. The distance between the end of the shadow and the top of the flag pole is 20 feet. Find the length of the shadow and the length of the flag pole, Round to the nearest tenth.The distance between opposite corners of a rectangular field is four more than the width of the field. The length of the field is twice its width, Find the distance between the opposite corners. Round to the nearest tenth.An arrow shot from the ground into the air at an initial speed of 108 ft/s. Use the formula h=16t2+v0t determine when the arrow will be 180 feet from the ground. Round the nearest tenth.A man throws a ball into the air with a velocity of 96 ft/s. Use the formula h=16t2+v0t to determine when the height of the ball will be 48 feet. Round to the nearest tenth.MaryAnne just returned from a visit with her grandchildren back east. The trip was 2400 miles from her home and her total time in the airplane for the round trip was 10 hours. If the plane was flying at a rate of 500 miles per hour, what was the speed of the jet stream?Gerry just returned from a cross country trip. The trip was 3000 miles from his home and his total time in the airplane for the round trip was 11 hours. If the plane was flying at a rate of 550 miles per hour, what was the speed of the jet stream?The weekly news magazine has a big story naming the Person of the Year and the editor wants the magazine to be printed as soon as possible. She has asked the printer to run an extra printing press to get the printing done more quickly, Press #1 takes 6 hours more than Press #2 to do the job and when both presses are running they can print the job in 4 hours. How long does it take for each press to print the job alone?Erlinda is having a party and wants to fill her hot tub. If she only uses the red hose it takes 3 hours more than if she only uses the green hose. If she uses both hoses together, the hot tub fills in 2 hours. How long does it take for each hose to fill the hot tub?In the following exercises, solve using any method. 195. The product of two consecutive odd numbers is 255. Find the numbers.In the following exercises, solve using any method. 196. The product of two consecutive even numbers is 360. Find the numbers.In the following exercises, solve using any method. 197. The product of two consecutive even numbers is 624. Find the numbers.In the following exercises, solve using any method. 198. The product of two consecutive odd numbers is 1,023. Find the numbers.In the following exercises, solve using any method. 199. The product of two consecutive odd numbers is 483. Find the numbers.In the following exercises, solve using any method. 200. The product of two consecutive even numbers is 528. Find the numbers.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 201. A triangle with area 45 square inches has a height that is two less than four times the base Find the base and height of the triangle.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 202. The base of a triangle is six more than twice the height. The area of the triangle is 88 square yards. Find the base and height of the triangle.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 203. The area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer that twice the height. What are the base and height of the triangle?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 204. A triangular banner for the basketball championship hangs in the gym. It has an area of 75 square feet. What is the length of the base and height, if the base is two-thirds of the height?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 205. The length of a rectangular driveway is five feet more than three times the width. The area is 50 square feet. Find the length and width of the driveway.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 206. A rectangular lawn has area 140 square yards. Its width that is six less than twice the length. What are the length and width of the lawn?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 207. A rectangular table for the dining room has a surface area of 24 square feet. The length is two more feet than twice the width of the table. Find the length and width of the table.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 208. The new computer has a surface area of 168 square inches. If the the width is 5.5 inches less that the length, what are the dimensions of the computer?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 209. The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is three feet. Find the lengths of the three sides of the triangle.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 210. The hypotenuse of a right triangle is 10 cm long. One of the triangle's legs is three times as the length of the other leg. Round to the nearest tenth. Find the lengths of the three sides of the triangle.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 211. A rectangular garden will be divided into two plots by fencing it on the diagonal. The diagonal distance from one corner of the garden to the opposite corner is five yards longer than the width of the garden. The length of the garden is three times the width. Find the length of the diagonal of the garden.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 212. Nautical flags are used to represent letters of the alphabet. The flag for the letter, O consists of a yellow right triangle and a red right triangle which are sewn together along their hypotenuse to form a square. The hypotenuse of the two triangles is three inches longer than a side of the flag. Find the length of the side of the flag.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 213. Gerry plans to place a 25-foot ladder against the side of his house to clean his gutters. The bottom of the ladder will be 5 feet from the house. How for up the side of the house will the ladder reach?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 214. John has a 10-foot piece of rope that he wants to use to support his 8-foot tree. How far from the base of the tree should he secure the rope?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 215. A firework rocket is shot upward at a rate of 640 ft/sec. Use the projectile formula h=16t2+v0t to determine when the height of the firework rocket will be 1200 feet.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 216. An arrow is shot vertically upward at a rate of 220 feet per second. Use the projectile formula h=16t2+v0t, to determine when height of the arrow will be 400 feet.In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 217. A bullet is fired straight up from a BB gun with initial velocity 1120 feet per second at an initial height of 8 feet. Use the formula h=16t2+v0t+8 to determine how many seconds it will take for the bullet to hit the ground. (That is, when will h = O?)In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 218. A stone is dropped from a 196-foot platform. Use the formulah=16t2+v0t+196 to determine how many seconds it will take for the stone to hit the ground. (Since the stone isdropped, v0=0. )In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 219. The businessman took a small airplane for a quick flight up the coast for a lunch meeting and then returned home. The plane flew a total of 4 hours and each way the trip was 200 miles. What was the speed of the wind that affected the plane which was flying at a speed of 120 mph?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. The couple took a small airplane for a quick flight up to the wine country for a romantic dinner and then returned home. The plane flew a total of 5 hours and each way the trip was 300 miles. If the plane was flying at 125 mph, what was the speed of the wind that affected the plane?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 221. Roy kayaked up the river and then back in a total time of 6 hours. The trip was 4 miles each way and the current was difficult. If Roy kayaked at a speed of 5 mph, what was the speed of the current?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 222. Rick paddled up the river, spent the night camping, and and then paddled back. He spent 10 hours paddling and the campground was 24 miles away. If Rick kayaked at a speed of 5 mph, what was the speed of the current?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 223. Two painters can paint a room in 2 hours if they work together. The less experienced painter takes 3 hours more than the more experienced painter to finish the job. How long does it take for each painter to paint the room individually?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 224. Two gardeners can do the weekly yard maintenance in 8 minutes if they work together. The older gardener takes 12 minutes more than the younger gardener to finish the job by himself. How long does it take for each gardener to do the weekly yard maintainence individually?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 225. It takes two hours for two machines to manufacture 10,000 parts. If Machine #1 can do the job alone in one hour less than Machine #2 can do the job, how long does it take for each machine to manufacture 1 0,000 parts alone?In the following exercises, solve using any method. Round your answers to the nearest tenth, if needed.. 226. Sully is having a party and wants to fill his swimming pool. If he only uses his hose it takes 2 hours more than if he only uses his neighbor's hose. If he uses both hoses together, the pool fills in 4 hours. How long does it take for each hose to fill the hot tub?Make up a problem involving the product of two consecutive odd integers. a. Start by choosing two consecutive odd integers. What are your integers? b. What is the product of your integers? c. Solve the equation n(n+2)=p,where p is the product you found in part (b). d. Did you get the numbers you started with?Make up a problem involving the product of two consecutive even integers. a. Start by choosing two consecutive even integers. What are your integers? b. What is the product of your integers? c. Solve the equation n(n+2)=p, where p is the product you found in part (b). d. Did you get the numbers you started with?Graph: f(x)=x2.Graph: f(x)=x2+1.Determine the whether the graph of each function is a parabola that opens upward or downward: a. f(x)=2x2+5x2 b. f(x)=3x24x+7 .Determine whether the graph of each of function is a parabola that opens upward or downward: a. f(x)=2x22x3 b. f(x)=5x22x1.For the graph of f(x)=2x28x+1 find: a. the axis of symmetry b. the vertex.For the graph f(x)=2x24x3 find: a. the axis of symmetry b. the vertex.Find the intercepts of the parabola whose function is f(x)=x2+2x8.Find the intercepts of the parabola whose function is f(x)=x24x12.Find the intercepts of the parabola whose function is f(x)=3x2+4x+4.Find the intercepts of the parabola whose function is f(x)=x24x5.Graph f(x)=x2+2x8 by using its properties.Graph f(x)=x28x+12 by using its properties.GRAPH f(x)=3x2+12x12 by using its properties.Graph f(x)=4x2+24x+36 by using its properties.Graph f(x)=x22x+3 by using its properties.Graph f(x)=3x26x4 by using its properties.Graph f(x)=5x2+10x+3 by using its properties.Graph f(x)=3x26x+5 by using its properties.Find the maximum or minimum value of the quadratic function f(x)=x28x+12.Find the maximum or minimum value of the quadratic functionf(x)=4x2+16x11.Solve, rounding answers to the nearest tenth. The quadratic function h(x)=16t2+128t+32 is used to find the height of a stone thrown upward from a height of 32 feet at a rate of 128 ft/sec. How long will it take for the stone to reach its maximum height? What is the maximum height?A path of a toy rocket thrown upward from the ground at a rate of 208 ft/sec is modeled by the quadratic function of. h(x)=16t2+208t. When will the rocket reach its maximum height? What will be the maximum height?In the following exercises, graph the functions by plotting points. 229. f(x)=x2+3 In the following exercises, graph the functions by plotting points. 230. f(x)=x23 In the following exercises, graph the functions by plotting points. 231. y=x2+1 In the following exercises, graph the functions by plotting points. 232. f(x)=x21 For each of the following exercises, determine if the parabola opens up or down. 233. a. f(x)=2x26x7 b. f(x)=6x2+2x+3 For each of the following exercises, determine if the parabola opens up or down. 234. a. f(x)=4x2+x4 b. f(x)=9x224x16 For each of the following exercises, determine if the parabola opens up or down. 235. a. f(x)=3x2+5x1 b. f(x)=2x24x+5 For each of the following exercises, determine if the parabola opens up or down. 236. a. f(x)=x2+3x4 b. f(x)=4x212x9 In the following functions, find (a) the equation of the axis of symmetry and (b) the vertex of its graph. 237. f(x)=x2+8x1 In the following functions, find (a) the equation of the axis of symmetry and (b) the vertex of its graph. 238. f(x)=x2+10x+25 In the following functions, find (a) the equation of the axis of symmetry and (b) the vertex of its graph. 239. f(x)=x2+2x+5 In the following functions, find (a) the equation of the axis of symmetry and (b) the vertex of its graph. 240. f(x)=2x28x3 In the following exercises, find the intercepts of the parabola whose function is given. 241. f(x)=x2+7x+6 In the following exercises, find the intercepts of the parabola whose function is given. 242. f(x)=x2+10x11 In the following exercises, find the intercepts of the parabola whose function is given. 243. f(x)=x2+8x+12 In the following exercises, find the intercepts of the parabola whose function is given. 244. f(x)=x2+5x+6 In the following exercises, find the intercepts of the parabola whose function is given. 245. f(x)=x2+8x19 In the following exercises, find the intercepts of the parabola whose function is given. 246. f(x)=3x2+x1 In the following exercises, find the intercepts of the parabola whose function is given. 247. f(x)=x2+6x+13 In the following exercises, find the intercepts of the parabola whose function is given. 248. f(x)=x2+8x+12 In the following exercises, find the intercepts of the parabola whose function is given. 249. f(x)=4x220x+25 In the following exercises, find the intercepts of the parabola whose function is given. 250. f(x)=x214x49 In the following exercises, find the intercepts of the parabola whose function is given. 251. f(x)=x26x9 In the following exercises, find the intercepts of the parabola whose function is given. 252. f(x)=4x2+4x+1 In the following exercises, graph the function by using its properties. 253. f(x)=x2+6x+5 In the following exercises, graph the function by using its properties. 254. f(x)=x2+4x12 In the following exercises, graph the function by using its properties. 255. f(x)=x2+4x+3 In the following exercises, graph the function by using its properties. 256. f(x)=x26x+8 In the following exercises, graph the function by using its properties. 257. f(x)=9x2+12x+4 In the following exercises, graph the function by using its properties. 258. f(x)=x2+8x16 In the following exercises, graph the function by using its properties. 259. f(x)=x2+2x7 In the following exercises, graph the function by using its properties. 260. f(x)=5x2+2 In the following exercises, graph the function by using its properties. 261. f(x)=2x24x+1 In the following exercises, graph the function by using its properties. 262. f(x)=3x26x1 In the following exercises, graph the function by using its properties. 263. f(x)=2x24x+2 In the following exercises, graph the function by using its properties. 264. f(x)=4x26x2 In the following exercises, graph the function by using its properties. 265. f(x)=x24x+2 In the following exercises, graph the function by using its properties. 266. f(x)=x2+6x+8 In the following exercises, graph the function by using its properties. 267. f(x)=5x210x+8 In the following exercises, graph the function by using its properties. 268. f(x)=16x2+24x9 In the following exercises, graph the function by using its properties. 269. f(x)=3x2+18x+20 In the following exercises, graph the function by using its properties. 270. f(x)=2x2+8x10 In the following exercises, find the maximum or minimum value of each function. 271. f(x)=2x2+x1 In the following exercises, find the maximum or minimum value of each function. 272. y=4x2+12x5 In the following exercises, find the maximum or minimum value of each function. 273. y=x26x+15 In the following exercises, find the maximum or minimum value of each function. 274. y=x2+4x5 In the following exercises, find the maximum or minimum value of each function. 275. y=9x2+16 In the following exercises, find the maximum or minimum value of each function. 276. y=4x249 In the following exercises, solve. Round answers to the nearest tenth. 277. An arrow is shot vertically upward from a platform 45 feet high at a rate of 168 ft/sec. Use the quadratic function h(t)=16t2+168t+45 find how long it will take the arrow to reach its maximum height, and then find the maximum height.In the following exercises, solve. Round answers to the nearest tenth. 278. A stone is thrown vertically upward from a platform that is 20 feet height at a rate of 160 ft/sec. Use the quadratic function h(t)=16t2+160t+20 to find how long it will take the stone to reach its maximum height, and then find the maximum height.In the following exercises, solve. Round answers to the nearest tenth. 279. A ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. Use the quadratic function h(t)=16t2+109t+0 to find how long it will take for the ball to reach its maximum height, and then find the maximum height.In the following exercises, solve. Round answers to the nearest tenth. 280. A ball is thrown vertically upward from the ground with an initial velocity of 122 ft/sec. Use the quadratic function h(t)=16t2+122t+0 to find how long it will take for the ball to reach its maxiumum height, and then find the maximum height.In the following exercises, solve. Round answers to the nearest tenth. 281. A computer store owner estimates that by charging x dollars each for a certain computer, he can sell 40x computers each week. The quadratic function R(x)=x2+40x is used to find the revenue, R, received when the selling price of a computer is x, Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.In the following exercises, solve. Round answers to the nearest tenth. 282. A retailer who sells backpacks estimates that by selling them for x dollars each, he will be able to sell 100x backpacks a month. The quadratic function R(x)=x2+100x is used to find the R, received when the selling price of a backpack is x. Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.In the following exercises, solve. Round answers to the nearest tenth. 283. A retailer who sells fashion boots estimates that by selling them for x dollars each, he will be able to sell 70x boots a week. Use the quadratic function R(x)=x2+70x to find the revenue received when the average selling price of a pair of fashion boots is x. Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.In the following exercises, solve. Round answers to the nearest tenth. 284. A cell phone company estimates that by charging x dollars each for a certain cell phone, they can sell 8x cell phones per day. Use the quadratic function R(x)=x2+8x to find the revenue received when the selling price of a cell phone is x. Find the selling price that will give them the maximum revenue, and then find the amount of the maximum revenue.In the following exercises, solve. Round answers to the nearest tenth. 285. A rancher is going to fence three sides of a corral next to a river. He needs to maximize the corral area using 240 feet of fencing. The quadratic equation A(x)=x(2402x) gives the area of the corral, A, for the length, x, of the corral along the river. Find the length of the corral along the river that will give the maximum area, and then find the maximum area of the corral.In the following exercises, solve. Round answers to the nearest tenth. 286. A veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic function A(x)=x(1002x) gives the area, A, of the dog run for the length, x, of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area, and then find the maximum area of the dog run.In the following exercises, solve. Round answers to the nearest tenth. 287. A land owner is planning to build a fenced in rectangular patio behind his garage, using his garage as one of the "walls." He wants to maximize the area using 80 feet of fencing. The quadratic function A(x)=x(802x) gives the area of the patio, where x is the width of one side. Find the maximum area of the patio.In the following exercises, solve. Round answers to the nearest tenth. 288. A family of three young children just moved into a house with a yard that is not fenced in. The previous owner gave them 300 feet of fencing to use to enclose part of their backyard. Use the quadratic function A(x)=x(3002x) to determine the maximum area of the fenced in yard.How do the graphs of the functions f(x)=x2 and f(x)=x21 differ? We graphed them at the start of this section. What is the difference between their graphs? How are their graphs the same?Explain the process of finding the vertex of a parabola.Explain how to find the intercepts of a parabola.How can you use the discriminant when you are graphing a quadratic function?a. Graph f(x)=x2,g(x)=x2+1, and h(x)=x21on the same rectangular coordinate system. b. Describe what effect adding a constant to the function has on the basic parabola.a. Graph f(x)=x2,g(x)=x2+6, and h(x)=x26 on the same rectangular coordinate system. b. Describe what effect adding a constant to the function has on the basic parabola.Graph f(x)=x25 using a vertical shift.Graph f(x)=x2+7 using a vertical shift.a. Graph f(x)=x2,g(x)=(x+2)2, and h(x)=(x2)2 on the same rectangular coordinate system. b. Describe what effect adding a constant to the function has on the basic parabola.a. Graph f(x)=x2,g(x)=x2+5, and h(x)=x25 on the same rectangular coordinate system. b. Describe what effect adding a constant to the function has on the basic parabola.Graph f(x)=(x4)2 using a horizontal shift.Graph f(x)=(x+6)2 using a horizontal shift.Graph f(x)=(x+2)23 using transformations.Graph f(x)=(x3)2+1 using transformations.Graph f(x)=3x2.Graph f(x)=2x2.Rewrite f(x)=4x28x+1 in the f(x)=a(xh)2+k form by completing the square.Rewrite f(x)=2x28x+3 in the f(x)=a(xh)2+k form by completing the square.Graph f(x)=x2+2x3 by using transformations.Graph f(x)=x28x+12 by using transformations.Graph f(x)=3x2+12x4 by using transformations.Graph f(x)=2x2+12x9 by using transformations.(a) Rewrite f(w)=3x26x+5 in f(x)=a(xh)2+k form and (b) graph the function using properties.(a) Rewrite f(x)=2x2+8x7 in f(x)=a(xh)2+k form and (b) graph the function using properties.Write the quadratic function in f(x)=a(xh)2+k form whose graph is shown.Determine the quadratic function whose graph is shown.In the following exercises, (a) graph the quadratic functions on the same rectangular coordinate system and (b) describe what effect adding a constant k, to the function has on the basic parabola. 293. f(x)=x2,g(x)=x2+4, and h(x)=x24 .In the following exercises, (a) graph the quadratic functions on the same rectangular coordinate system and (b) describe what effect adding a constant k, to the function has on the basic parabola. 294. f(x)=x2,g(x)=x2+7, and h(x)=x27.In the following exercises, graph each function using a vertical shift. 295. f(x)=x2+3 In the following exercises, graph each function using a vertical shift. 296. f(x)=x27 In the following exercises, graph each function using a vertical shift. 297. g(x)=x2+2 In the following exercises, graph each function using a vertical shift. 298. g(x)=x2+5 In the following exercises, graph each function using a vertical shift. 299. h(x)=x24 In the following exercises, graph each function using a vertical shift. 300. h(x)=x25 In the following exercises, (a) graph the quadratic functions on the same rectangular coordinate system and (b) describe what effect adding a constant, h, to the function has on the basic parabola. 301. f(x)=x2,g(x)=(x3)2, and h(x)=(x+3)2.In the following exercises, (a) graph the quadratic functions on the same rectangular coordinate system and (b) describe what effect adding a constant, h, to the function has on the basic parabola. 302. f(x)=x2,g(x)=(x+4)2, and h(x)=(x4)2.In the following exercises, graph each function using a horizontal shift. 303. f(x)=(x2)2 In the following exercises, graph each function using a horizontal shift. 304. f(x)=(x1)2 In the following exercises, graph each function using a horizontal shift. 305. f(x)=(x+5)2 In the following exercises, graph each function using a horizontal shift. 306. f(x)=(x+3)2 In the following exercises, graph each function using a horizontal shift. 307. f(x)=(x5)2 In the following exercises, graph each function using a horizontal shift. 308. f(x)=(x+2)2 In the following exercises, graph each function using transformations. 309. f(x)=(x+2)2+1 In the following exercises, graph each function using transformations. 310. f(x)=(x+4)2+2 In the following exercises, graph each function using transformations. 311. f(x)=(x1)2+5 In the following exercises, graph each function using transformations. 312. f(x)=(x3)2+4 In the following exercises, graph each function using transformations. 313. f(x)=(x+3)21 In the following exercises, graph each function using transformations. 314. f(x)=(x+5)22 In the following exercises, graph each function using transformations. 315. f(x)=(x4)23 In the following exercises, graph each function using transformations. 316. f(x)=(x6)22 In the following exercises, graph each function. 317. f(x)=2x2 In the following exercises, graph each function. 318. f(x)=4x2 In the following exercises, graph each function. 319. f(x)=4x2 In the following exercises, graph each function. 320. f(x)=x2 In the following exercises, graph each function. 321. f(x)=12x2 In the following exercises, graph each function. 322. f(x)=13x2 In the following exercises, graph each function. 323. f(x)=14x2 In the following exercises, graph each function. 324. f(x)=12x2 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 325. f(x)=3x212x5 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 326. f(x)=2x212x+7 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 327. f(x)=3x2+6x1 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 328. f(x)=4x216x9 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 329. f(x)=x2+6x+5 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 330. f(x)=x2+4x12 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 331. f(x)=x2+4x12 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 332. f(x)=x26x+8 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 333. f(x)=x26x+15 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 334. f(x)=x2+8x+10 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 335. f(x)=x2+8x16 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 336. f(x)=x2+2x7 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 337. f(x)=x24x+2 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 338. f(x)=x2+4x5 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 339. f(x)=5x210x+8 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 340. f(x)=3x2+18x+20 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 341. f(x)=2x24x+1 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 342. f(x)=3x26x1 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 343. f(x)=2x2+8x10 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 344. f(x)=3x2+6x+1 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 345. f(x)=2x2+4x+6 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 346. f(x)=3x212x+7 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 347. f(x)=x2+2x4 In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the square. 348. f(x)=2x24x5 In the following exercises, math the graphs to one of the following functions: (a) f(x)=x2+4 (b) f(x)=x24 (c) f(x)=(x+4)2 (d) f(x)=(x4)2 (e) f(x)=(x+4)24 (f) f(x)=(x+4)2+4 (g) f(x)=(x4)24 (h) f(x)=(x4)2+4 In the following exercises, math the graphs to one of the following functions: (a) f(x)=x2+4 (b) f(x)=x24 (c) f(x)=(x+4)2 (d) f(x)=(x4)2 (e) f(x)=(x+4)24 (f) f(x)=(x+4)2+4 (g) f(x)=(x4)24 (h) f(x)=(x4)2+4 In the following exercises, math the graphs to one of the following functions: (a) f(x)=x2+4 (b) f(x)=x24 (c) f(x)=(x+4)2 (d) f(x)=(x4)2 (e) f(x)=(x+4)24 (f) f(x)=(x+4)2+4 (g) f(x)=(x4)24 (h) f(x)=(x4)2+4 In the following exercises, math the graphs to one of the following functions: (a) f(x)=x2+4 (b) f(x)=x24 (c) f(x)=(x+4)2 (d) f(x)=(x4)2 (e) f(x)=(x+4)24 (f) f(x)=(x+4)2+4 (g) f(x)=(x4)24 (h) f(x)=(x4)2+4 In the following exercises, math the graphs to one of the following functions: (a) f(x)=x2+4 (b) f(x)=x24 (c) f(x)=(x+4)2 (d) f(x)=(x4)2 (e) f(x)=(x+4)24 (f) f(x)=(x+4)2+4 (g) f(x)=(x4)24 (h) f(x)=(x4)2+4 In the following exercises, math the graphs to one of the following functions: (a) f(x)=x2+4 (b) f(x)=x24 (c) f(x)=(x+4)2 (d) f(x)=(x4)2 (e) f(x)=(x+4)24 (f) f(x)=(x+4)2+4 (g) f(x)=(x4)24 (h) f(x)=(x4)2+4 In the following exercises, math the graphs to one of the following functions: (a) f(x)=x2+4 (b) f(x)=x24 (c) f(x)=(x+4)2 (d) f(x)=(x4)2 (e) f(x)=(x+4)24 (f) f(x)=(x+4)2+4 (g) f(x)=(x4)24 (h) f(x)=(x4)2+4

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