# What is the vertex form of y= 2x^2+4x-30 ?

Jan 18, 2016

$y = 2 {\left(x + 1\right)}^{2} - 32$

#### Explanation:

The vertex form

$y = a {\left(x - h\right)}^{2} + k$ where $\left(h , k\right)$ is the vertex.

Our question $y = 2 {x}^{2} + 4 x - 30$

We got different approaches for getting to the vertex form.
One is to use the formula for $x$coordinate of the vertex and then using the value to find the $y$ coordinate and write the given equation in the vertex form.

We are going to use a different approach. Let us use completing the square.

$y = 2 {x}^{2} + 4 x - 30$

We would first write the given equation in the following way.

$y = \left(2 {x}^{2} + 4 x\right) - 30$ As you can see we have grouped the first and the second terms.

$y = 2 \left({x}^{2} + 2 x\right) - 30$ Here 2 has been factored out from the grouped term.

Now take the$x$ coefficient and divide it by $2$. Square the result. This should be added and subtracted within the parenthesis.

$y = 2 \left({x}^{2} + 2 x + {\left(\frac{2}{2}\right)}^{2} - {\left(\frac{2}{2}\right)}^{2}\right) - 30$
$y = 2 \left({x}^{2} + 2 x + 1 - 1\right) - 30$
y=2(x+1)^2-1)-30 Note ${x}^{2} + 2 x + 1 = \left(x + 1\right) \left(x + 1\right)$
$y = 2 {\left(x + 1\right)}^{2} - 2 - 30$ Distributed the $2$ and removed the parenthesis.

$y = 2 {\left(x + 1\right)}^{2} - 32$ The vertex form.