8. Consider the function (x) = x² - 8x³ + 18x² - 27, and in factored form: f(x) = (x + 1)(x − 3)³ a) Determine the x and y-intercepts. - b) Determine the coordinates and nature of the critical points. c) Determine the intervals of increase and decrease. d) Determine the coordinates of the inflection points. e) Determine the intervals of concavity. f) Graph the function on the grid below. (Label axes appropriately)

Describe the end behavior of each polynomial. (a) y=x38x2+2x15 End behavior: y as x y as x (b) y=2x4+12x+100 End behavior: y as x y as x

Find the intercepts of x+4y=8 .

Find the x and y-intercepts for the following: 2x5y=6 .

A company that makes and sells baseball caps has found that the total monthly cost C in dollars of producing x caps is given by the function C(x)=0.2x280x+9000. Find the production level that will minimize the monthly cost and find the minimum cost.

2. Let fx) = - 10 (x+ 2 )² (x – 3)(x + 2)*. Do not use your calculator until part d. a. List the factors and the x-intercepts (zeros) of f(x). In the right column, circle either touch or passthrough describing what the graph will do at each x-intercept. appearance at x-intercept touch pass-through factor x-intercept at x = ? touch pass-through touch pass-through b. What are the degree and the leading coefficient? degree: leading coefficient: c. What are the end behaviors (up or down)? left end: right end: d. Now graph f(x) on your calculator. Adjust the window until you can see all of the features listed above. D Then, sketch the screen.

b) Plot the quadratic y = -2x² + 8x -8, where 0 ≤ x ≤ 4.

Determine b and c for the quadratic function f(x) = −x2 + bx + c where the y-intercept is2 and it goes through the point (−1,5)

5. Use the function f(x) = x³ + 2x² + x - 2, create a table with 8 inputs and outputs. Complete the triangular differences until you have a common difference. Lastly explain what the result reveals.

Julie has tracked Bouncy Ball company profits for severalyears, and her analysis has determined that the function,P(x) = –3x3 + 138x2 + 588x + 600, can be used to determineprofits, in dollars, every year for x years after 1980. 1) Find the y–intercept for the profit function and give an interpretation. 2) Determine the end behavior of the profit function.a) What is the behavior at the left end? Is this behavior relevant tocompany profits? If so, what does it say about company profits asx → – ∞? b) What is the behavior at the right end? Is this behavior relevant tocompany profits? If so, what does it say about company profits asx → ∞? 3) We will use the Rational Zeros Theorem to determine possible rational zerosof P(x). First, factor out the common factor of -3. 4) Use synthetic division to find at least one rational zero of P(x). Chapter 5: Polynomial Functions 69Profitable Venture Page 2 of 25) Use the zero found in item 4) along with the quotient to completely factorP(x). 6) What are…