# What is the vertex form of y=(x – 12)(x + 4) ?

Dec 14, 2015

$y = {\left(x - 4\right)}^{2} - 64$

#### Explanation:

First, distribute the binomials terms.

$y = {x}^{2} + 4 x - 12 x - 48$

$y = {x}^{2} - 8 x - 48$

From here, complete the square with the first two terms of the quadratic equation.

Recall that vertex form is $y = a {\left(x - h\right)}^{2} + k$ where the vertex of the parabola is at the point $\left(h , k\right)$.

$y = \left({x}^{2} - 8 x \textcolor{red}{+ 16}\right) - 48 \textcolor{red}{- 16}$

Two things just happened:

The $16$ was added inside the parentheses so that a perfect square term will be formed. This is because $\left({x}^{2} - 8 x + 16\right) = {\left(x - 4\right)}^{2}$.

The $- 16$ was added outside the parentheses to keep the equation balanced. There is a net change of $0$ now thanks to the addition of $16$ and $- 16$, but the face of the equation is changed.

Simplify:

$y = {\left(x - 4\right)}^{2} - 64$

This tells us that the parabola has a vertex at $\left(4 , - 64\right)$. graph{(x-12)(x+4) [-133.4, 133.5, -80, 40]}