# How do you find the vertex of  f(x)= -2x^2 + 16x +4?

Nov 15, 2016

The vertex form is $= - 2 {\left(x - 4\right)}^{2} + 36$

#### Explanation:

Let's complete the squares

$f \left(x\right) = - 2 {x}^{2} + 16 x + 4$

$= - 2 \left({x}^{2} - 8 x\right) + 4$

$= - 2 \left({x}^{2} - 8 x + 16\right) + 4 + 32$

$= - 2 {\left(x - 4\right)}^{2} + 36$

The vertex form is $= - 2 {\left(x - 4\right)}^{2} + 36$

The vertex is $\left(4 , 36\right)$

The axis of symmetry is $x = 4$

graph{-2(x-4)^2+36 [-69.2, 62.56, -1, 64.87]}