Explanation The graph of the quadratic equation y = a x 2 + b x + c is carried by find the ordered pair solution of the given equation by choosing some appropriate value of x . thereby finding the value of y . then plot the ordered pairs and joined the plots which gives, the graph of y = a x 2 + b x + c is a smooth curve through the plotted points. This curve is called a parabola. Here, the vertex considered by the lowest point on a parabola in opening upward and the highest point on a parabola in opening downward and the vertex formula of the parabola y = a x 2 + b x + c has x -coordinates − b 2 a . Find the intercepts: Let x = 0 and solve for y to find the y -intercepts. Let y = 0 and solve for x to find the x -intercepts. Calculation: Given, y = 2 − x 2 Find the ordered pair’s solutions of the above equation by choosing some appropriate value for x , thereby finding the value of y . When, x = − 4 y = 2 − ( − 4 ) 2 = 2 − ( − 4 ⋅ − 4 ) = 2 − ( 16 ) = − 14 Thus, the ordered pair solution is ( − 4 , − 14 ) When, x = − 3 y = 2 − ( − 3 ) 2 = 2 − 9 = − 7 Thus, the ordered pair solution is ( − 3 , − 7 ) When, x = − 2 y = 2 − ( − 2 ) 2 = 2 − ( − 2 ⋅ − 2 ) = 2 − ( 4 ) = − 2 Thus, the ordered pair solution is ( − 2 , − 2 ) When, x = − 1 y = 2 − ( − 1 ) 2 = 2 − ( − 1 ⋅ − 1 ) = 2 − 1 = 1 Thus, the ordered pair solution is ( − 1 , 1 ) When, x = 0 y = 2 − ( 0 ) 2 = 2 − 0 = 2 Thus, the ordered pair solution is ( 0 , 2 ) When, x = 1 y = 2 − ( 1 ) 2 = 2 − ( 1 ⋅ 1 ) = 2 − 1 = 1 Thus, the ordered pair solution is ( 1 , 1 ) When, x = 2 y = 2 − ( 2 ) 2 = 2 − ( 2 ⋅ 2 ) = 2 − ( 4 ) = − 2 Thus, the ordered pair solution is ( 2 , − 2 ) When, x = 3 y = 2 − ( 3 ) 2 = 2 − ( 3 ⋅ 3 ) = 2 − 9 = − 7 Thus, the ordered pair solution is ( 3 , − 7 ) When, x = 4 y = 2 − ( 4 ) 2 = 2 − ( 4 ⋅ 4 ) = 2 − 16 = − 14 Thus, the ordered pair solution is ( 4 , − 14 ) The obtained ordered pair is tabulated as. x y − 4 − 14 − 3 − 7 − 2 − 2 − 1 1 0 2 1 1 2 − 2 3 − 7 4 − 14 Thus, we need to plot to the knowing ordered pair to obtain to graph

Prealgebra & Introductory Algebra (4th Edition)

4th Edition

ISBN: 9780321955791

Author: Elayn Martin-Gay

Publisher: PEARSON

See similar textbooks

Question

Chapter 16.4, Problem 15E

To determine

To sketch:

To sketch the graph

y=2−x2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.4, Problem 14E

Chapter 16.4, Problem 16E

Students have asked these similar questions

0 5 -1 2 1 N = 1 to x = 3 Based on the graph above, estimate to one decimal place the average rate of change from x =

Complete the description of the piecewise function graphed below. Use interval notation to indicate the intervals. -7 -6 -5 -4 30 6 5 4 3 0 2 1 -1 5 6 + -2 -3 -5 456 -6 - { 1 if x Є f(x) = { 1 if x Є { 3 if x Є

Mathematics Mastery Quiz Instructions: • No partial credit will be awarded; any mistake will result in a score of 0. Submit your solution before the deadline. Ensure your solution is detailed and all steps are well-documented. Problem Let the function f(x, y) = x²y³ - 3x+y+ety and consider the following tasks: 1. [Critical Points and Classification] a. Find all critical points of f(x, y). b. Use the second partial derivative test to classify each critical point as a local minimum, local maximum, or saddle point. 2. [Line Integral Evaluation] Consider the vector field F(x, y) = (2x³y - y³ + e², 3x²y² - 4x³ + e³). a. Verify whether F is conservative. b. If conservative, compute the line integral of F along the curve C, parameterized as: C: Sx(t) = t² [y(t) = ln(t + 1)' tЄ [0,1].

Chapter 16 Solutions

Prealgebra & Introductory Algebra (4th Edition)

Ch. 16.1 - Prob. 1P Ch. 16.1 - Prob. 2P Ch. 16.1 - Prob. 3P Ch. 16.1 - Prob. 4P Ch. 16.1 - Prob. 5P Ch. 16.1 - Prob. 6P Ch. 16.1 - Prob. 7P Ch. 16.1 - Prob. 8P Ch. 16.1 - Prob. 9P Ch. 16.1 - Prob. 1E

Knowledge Booster

To sketch the graph y = 2 − x 2

To sketch: To sketch the graph y=2−x2

Want to see the full answer?

Chapter 16 Solutions

To sketch:

To sketch the graph

y=2−x2