Question

Plot the axis of symmetry and the vertex for this function: h(x) = (x − 5)2 − 7.

Answer 1

The vertex and the axis of symmetry in the attached figure

Explanation:

we know that

The equation of a vertical parabola written in vertex form is equal to

`f(x)=a(x-h)^2+k`

where

a is the leading coefficient

(h,k) is the vertex of the parabola

and the equation of the axis of symmetry is equal to the x-coordinate of the vertex

`x=h`

In this problem

we have

`h(x)=(x-5)^2-7`

This is a vertical parabola written in vertex form open upward

The vertex is a minimum

where

the vertex is the point (5,-7)

the x-coordinate of the vertex is 5

so

the equation of the axis of symmetry is equal to

`x=5`

The graph in the attached figure