# What is the vertex form of y=x^2+2x+15?

Jan 10, 2016

$y = {\left(x + 1\right)}^{2} + 14$

#### Explanation:

Given _

$y = {x}^{2} + 2 x + 15$

The vertex form of the equation is -

$y = a {\left(x - h\right)}^{2} + k$

If we know the values of $a , h \mathmr{and} k$ we can change the given equation into a vertex form.

Find the vertex $\left(h , k\right)$

$a$ is the coefficient of ${x}^{2}$
$h$ is the x-co-ordinate of the vertex
$k$ is the y-co-ordinate of the vertex

$a = 1$
$h = \frac{- b}{2 a} = \frac{- 2}{2 \times 1} = - 1$

$k = {\left(- 1\right)}^{2} + 2 \left(- 1\right) + 15 = 1 - 2 + 15 = 14$

Now substitute the values of $a , h \mathmr{and} k$ in the vertex form of the equation.

$y = \left(1\right) {\left(x - \left(- 1\right)\right)}^{2} + 14$
$y = {\left(x + 1\right)}^{2} + 14$