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

May 19, 2018

$\textcolor{red}{v e r t e x = \left(h , k\right) = \left(4 , 8\right)}$

the axis of symmetry $\textcolor{red}{x = h = 4}$

#### 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 $\textcolor{b l u e}{y = - {\left(x - 4\right)}^{2} + 8}$

$h = 4 \mathmr{and} k = 8$

$\textcolor{red}{v e r t e x = \left(h , k\right) = \left(4 , 8\right)}$

the axis of symmetry $\textcolor{red}{x = h = 4}$

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]}