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. Find the vertex: 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 = − 1 3 x 2 Find the ordered pairs solutions of the above equation by choosing some appropriate value for x , thereby finding the value of y . When x = − 9 y = − 1 3 ( − 9 ) 2 = − 1 3 ( − 9 ⋅ − 9 ) = − 1 1 ( − 3 ⋅ − 9 ) y = − 27 Thus, the ordered pair solution is ( − 9 , − 27 ) When x = − 6 y = − 1 3 ( − 6 ) 2 y = − 1 3 ( − 6 ⋅ − 6 ) y = − 1 ( − 2 ⋅ − 6 ) y = − 12 Thus, the ordered pair solution is ( − 6 , − 12 ) When x = − 3 y = − 1 3 ( − 3 ) 2 = − 1 3 ( − 3 ⋅ − 3 ) y = − 3 Thus, the ordered pair solution is ( 3 , − 3 ) When x = 6 y = − 1 3 ( 6 ) 2 = − 1 3 ( 6 ⋅ 6 ) y = − 12 Thus, the ordered pair solution is ( 6 , − 12 ) When x = 9 y = − 1 3 ( 9 ) 2 = − 1 2 ( 9 ⋅ 9 ) y = − 27 Thus, the ordered pair solution is ( 9 , − 27 ) The obtained ordered pair is tabulated as x y − 9 − 27 − 6 − 12 − 3 − 3 0 0 3 − 3 6 − 12 9 − 27 Thus, we need to plot the following ordered pairs to obtain the graph

Prealgebra & Introductory Algebra (4th Edition)

4th Edition

ISBN: 9780321955791

Author: Elayn Martin-Gay

Publisher: PEARSON

See similar textbooks

Question

Chapter 16.4, Problem 24E

To determine

To sketch the graph:

y=−13x2

Also to label vertices and the intercepts

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.4, Problem 23E

Chapter 16.4, Problem 25E

Students have asked these similar questions

Please give a handwritten solution without use of AI

Q4) (i) Calculate the fourier transform of : h(t) 2T (is) h(t) 2T -T о T 2T ·(-++T). cos2t ost≤T (iii) hro (4) ((-++T). cos otherwise

1. Sketch the following piecewise function on the graph. (5 points) x<-1 3 x² -1≤ x ≤2 f(x) = = 1 ४ | N 2 x ≥ 2 -4- 3 2 -1- -4 -3 -2 -1 0 1 -1- --2- -3- -4- -N 2 3 4

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 = − 1 3 x 2 Also to label vertices and the intercepts

To sketch the graph: y=−13x2 Also to label vertices and the intercepts

Want to see the full answer?

Chapter 16 Solutions

To sketch the graph:

y=−13x2

Also to label vertices and the intercepts