Chapter 9, Problem 22SGR

To determine

To find: An equation for the function shown in the graph.

Answer to Problem 22SGR

The equation of given parabola is $y=2x^2-3$

Explanation of Solution

Given Information: Given a graph of a parabola

The vertex form of a parabola is

  $\begin{array}{l}$ y=a{(x-h)}^2+k$vertexis(0,-3)=(h,k)\end{array}$

Therefore put h = 0 and k = -3

  $\begin{array}{l}$ y=a{(x-0)}^2-3$y=a{x}^2-3\end{array}$

The parabola is passing through (1,-1) so put x = 1 and y = -1

  $\begin{array}{l}$ -1=a{(1)}^2-3$-1=a-3\\ -1+3=a\\ a=2\end{array}$

Put the value of an in equation(1)

  $y=2x^2-3$

Thus the equation of a given parabola is

  $y=2x^2-3$