# What is the vertex form of x= 4y^2 + 16y + 16?

Jul 25, 2017

See a solution process below:

#### Explanation:

To convert a quadratic from $x = a {y}^{2} + b y + c$ form to vertex form, $x = a {\left(y - \textcolor{red}{h}\right)}^{2} + \textcolor{b l u e}{k}$, you use the process of completing the square.

This equation is already a perfect square. We can factor out a $4$ and complete the square:

$x = 4 {y}^{2} + 16 y + 16 - \textcolor{red}{16}$

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

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

Or, in precise form:

$x = 4 {\left(y + \left(- 2\right)\right)}^{2} + 0$