Chapter 9, Problem 8CR

To determine

The graph of the function.

The axis of symmetry and the vertex.

Answer to Problem 8CR

The vertex of the parabola will be: $\left(0,8\right)$

The axis of symmetry will be $x=0$

Explanation of Solution

Given:

The given function is:

  $y=5x^2+8$

Calculation:

Compare the equation with $y=a{x}^2+bx+c$

  $a=5,b=0,c=8$

The x-coordinate of the vertex will be:

  $\begin{array}{l}x=-\frac{b}{2a}\\ x=-\frac{0}{2\left(5\right)}\\ x=0\end{array}$

The y-coordinate of the vertex will be:

  $\begin{array}{l}y=5x^2+8\\ y=5{\left(0\right)}^2+8\\ y=8\end{array}$

The vertex of the parabola will be: $\left(0,8\right)$

If $V\left(h,k\right)$ is the vertex, then the axis of symmetry will be $x=h$ , therefore, the axis of symmetry will be $x=0$

The graph will be: