# How do you write the vertex form equation of the parabola y = -2(x+4)(x-2)?

Apr 17, 2017

#### Explanation:

Given: $y = - 2 \left(x + 4\right) \left(x - 2\right)$

Multiply the factors:

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

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

$y = - 2 {x}^{2} - 4 x + 16 \text{ [1]}$

Please observe that equation [1] is in the standard form $y = a {x}^{2} + b x + c$ where $a = - 2 , b = - 4 \mathmr{and} c = 16$

The vertex form of a parabola of this type is:

$y = a {\left(x - h\right)}^{2} + k \text{ [2]}$

The "a" in the standard form and the "a" in the vertex form are the same attribute of the parabola, therefore, substitute -2 for "a" into equation [2]:

$y = - 2 {\left(x - h\right)}^{2} + k \text{ [3]}$

We know that $h = - \frac{b}{2 a}$:

h = -(-4)/(2(-2)

$h = - 1$

Substitute -1 for h into equation [3]:

$y = - 2 {\left(x - - 1\right)}^{2} + k \text{ [4]}$

Evaluate equation [1] at $x = 0$

$y = 16$

Evaluate equation [4] and x = 0 and y = 16, then solve for k:

$16 = - 2 {\left(1\right)}^{2} + k$

$k = 18$

The vertex form is:

$y = - 2 {\left(x - - 1\right)}^{2} + 18 \text{ [5]}$