# What is the vertex form of y=5x^2+17x+13 ?

Nov 22, 2017

When given an equation of the form:

$y = a {x}^{2} + b x + c$

The vertex form is:

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

where $h = - \frac{b}{2 a} \mathmr{and} k = a {h}^{2} + b h + c$

#### Explanation:

Given:

$y = 5 {x}^{2} + 17 x + 13$

Please observe that $a = 5 , b = 17 , \mathmr{and} c = 13$

Substitute 5 for a in the vertex form:

$y = 5 {\left(x - h\right)}^{2} + k$

Compute the value of h:

$h = - \frac{17}{2 \left(5\right)}$

$h = - \frac{17}{10}$

Substitute the value of h into the vertex form:

$y = 5 {\left(x - \left(- \frac{17}{10}\right)\right)}^{2} + k$

Compute the value of k:

$k = 5 {\left(- \frac{17}{10}\right)}^{2} + 17 \left(- \frac{17}{10}\right) + 13$

$k = - \frac{29}{20}$

Substitute the value of k into the vertex form:

$y = 5 {\left(x - \left(- \frac{17}{10}\right)\right)}^{2} + \left(- \frac{29}{20}\right)$

The above equation is the vertex form.