# What is the vertex of  y=-3x^2-4x+2(x-2)^2 ?

Dec 23, 2015

(4,24)

#### Explanation:

Simplify first
$y = - 3 {x}^{2} - 4 x + 2 {\left(x - 2\right)}^{2}$
$y = - 3 {x}^{2} - 4 x + 2 \left({x}^{2} + 4 x + 4\right)$
$y = - 3 {x}^{2} - 4 x + 2 {x}^{2} + 8 x + 8$
$y = - {x}^{2} + 8 x + 8$

Now to solve for the vertex algebraically , we use the formula
Vertex= $\left(- \frac{b}{2 a} , f \left(- \frac{b}{2 a}\right)\right)$
$- \frac{b}{2 a} = 4$
$f \left(4\right) = 24$

Vertex = (4,24)