# The graph of y=(2x -4)(x+ 4) is a parabola in the plane. How do you find the standard and vertex form?

Oct 20, 2016

The vertex form is $y = 2 \left({\left(x + 1\right)}^{2} - 9\right)$

#### Explanation:

Expand the equation
$y = \left(2 x - 4\right) \left(x + 4\right) = 2 {x}^{2} + 4 x - 16$
Then complete the squares for ${x}^{2} + 2 x$
$y = 2 \left({x}^{2} + 2 x - 8\right) = 2 \left({x}^{2} + 2 x + 1 - 8 - 1\right)$
$y = 2 \left({\left(x + 1\right)}^{2} - 9\right)$
So the line of symmetry has equation $x = - 1$
and the vertex is at $\left(- 1 , - 18\right)$
graph{2(x^2)+4x-16 [-40, 40, -20, 20]}