Chapter 11.8, Problem 12MRE

To determine

To find: The coordinates of the vertex and the equation of the axis of symmetry.

Answer to Problem 12MRE

The coordinate of the vertex is $\left(0,5\right)$ and the equation of the symmetry is $x=0$ .

Explanation of Solution

Given information:

The given equation is,

  $y=5-2x^2$

The x-coordinate of the vertex is calculated as,

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

The y-coordinate of the vertex is calculated as,

  $\begin{array}{l}y=5-2x^2\\ y=5-2{\left(0\right)}^2\\ y=5\end{array}$

The coordinate of the vertex is $\left(0,5\right)$ .

The equation of axis of the symmetry is calculated as,

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

Thus, the coordinate of the vertex is $\left(0,5\right)$ and the equation of the symmetry is $x=0$ .