Chapter 8.8, Problem 20WE

To determine

To find: Thecoordinates of the vertex, the equation of the axis of symmetry and the graph of the function.

Answer to Problem 20WE

The coordinate of the vertex is $\left(0,3\right)$ and the equation of the symmetry is $x=0$ .

Explanation of Solution

Given information:

The given equation is,

  $y=3-x^2$

The x -coordinate of the vertex is calculated as,

  $\begin{array}{c}x=-\frac{b\left(\text{coefficent of }x\right)}{2a\left(\text{coefficent of }{x}^2\right)}\\ =-\frac{\left(0\right)}{2\left(-1\right)}\\ =0\end{array}$

The y -coordinate of the vertex is calculated as,

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

The coordinate of the vertex is $\left(0,3\right)$ .

The equation of axis od symmetry is calculated as,

  $\begin{array}{c}x=-\frac{b\left(\text{coefficent of }x\right)}{2a\left(\text{coefficent of }{x}^2\right)}\\ =-\frac{\left(0\right)}{2\left(-1\right)}\\ x=0\end{array}$

Consider the graph of the given equation,

  

Thus, the coordinate of the vertex is $\left(0,3\right)$ and the equation of the symmetry is $x=0$ .