# What is the vertex form y=x^2+2x-8?

Oct 30, 2016

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

#### Explanation:

Changing a quadratic function from standard form to vertex form actually requires that we go through the process of completing the square. To do this, we need the ${x}^{2}$ and $x$ terms only on the right side of the equation.

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

Now, the right side has the $a {x}^{2} + b x$ terms, and we need to find $c$, using the formula $c = {\left(\frac{b}{2}\right)}^{2}$.

In our prepared equation, $b = 2$, so
$c = {\left(\frac{2}{2}\right)}^{2} = {1}^{2} = 1$

Now, we add $c$ to both sides of our equation, simplify the left side, and factor the right side.

$y + 8 + 1 = {x}^{2} + 2 x + 1$
$y + 9 = {\left(x + 1\right)}^{2}$

To finish putting the equation in vertex form, subtract $9$ from both sides, thus isolating the $y$:

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