# What is the vertex form of y= y=x^2+5x-36?

The vertex form $y - - \frac{169}{4} = {\left(x - - \frac{5}{2}\right)}^{2}$
with vertex at $\left(h , k\right) = \left(- \frac{5}{2} , - \frac{169}{4}\right)$

#### Explanation:

From the given equation $y = {x}^{2} + 5 x - 36$

complete the square

$y = {x}^{2} + 5 x - 36$
$y = {x}^{2} + 5 x + \frac{25}{4} - \frac{25}{4} - 36$

We group the first three terms

$y = \left({x}^{2} + 5 x + \frac{25}{4}\right) - \frac{25}{4} - 36$

$y = {\left(x + \frac{5}{2}\right)}^{2} - \frac{25}{4} - \frac{144}{4}$

$y = {\left(x + \frac{5}{2}\right)}^{2} - \frac{169}{4}$

$y - - \frac{169}{4} = {\left(x - - \frac{5}{2}\right)}^{2}$

graph{y+169/4=(x--5/2)^2[-100, 100,-50,50]}

God bless...I hope the explanation is useful.

Mar 31, 2016

$y = {\left(x + \frac{5}{2}\right)}^{2} - \frac{169}{4}$

#### Explanation:

x-coordinate of vertex:
$x = - \frac{b}{2 a} = - \frac{5}{2}$
y-coordinate of vertex:
$y \left(- \frac{5}{2}\right) = \left(\frac{25}{4}\right) - \frac{25}{2} - 36 = - \frac{25}{4} - 36 = - \frac{169}{4.}$
$V e r t e x \left(- \frac{5}{2} , - \frac{169}{4}\right)$
Vertex form: $y = {\left(x + \frac{5}{2}\right)}^{2} - \frac{169}{4}$