Chapter 8.8, Problem 7WE

To determine

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

Answer to Problem 7WE

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

Explanation of Solution

Given information:

The given equation is,

  $f\left(x\right)=x^2-5$

The x -coordinate of the vertex is calculated as,

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

The y -coordinate of the vertex is calculated as,

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

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

The equation of axisod symmetry is calculated as,

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

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