Question

How do you graph and label the vertex and axis of symmetry of `y=-(x-4)^2+8`?

Answer 1

`color(red)[vertex=(h, k)=(4,8)]`

the axis of symmetry `color(red)[x=h=4]`

Explanation:

The vertex form of a quadratic function is given by

`color(blue)[y=a(x−h)2+k]`

where (h, k) is the vertex of the parabola.

when written in vertex form

(h, k) is the vertex of the parabola and x = h is the axis of symmetry

the h represents a horizontal shift (how far left, or right the graph has shifted from x = 0)

the k represents a vertical shift (how far up, or down the graph has shifted from y = 0)

the vertex of `color(blue)[y=-(x-4)^2+8]`

`h=4 and k=8`

`color(red)[vertex=(h, k)=(4,8)]`

the axis of symmetry `color(red)[x=h=4]`

show the vertex and the axis if symmetry in the graph below

graph{y=-(x-4)^2+8 [-12.34, 16.14, -2.62, 11.62]}