# What is the vertex form of y= 5x^2 + 5x -12 ?

Mar 5, 2018

$v e r t e x = \left(- \frac{1}{2} , - 13.25\right)$

#### Explanation:

$y = 5 {x}^{2} + 5 x - 12$

take 5 as a common factor from the first two terms

$y = 5 \left({x}^{2} + x\right) - 12$

completing square

$y = 5 \left({x}^{2} + x + {\left(\frac{1}{2}\right)}^{2}\right) - 12 - \frac{5}{4}$

for completing square you take half the coefficient of x and square it
and we subtract 5/4 because from completing square we get 1/4 so 1/4 times 5 is 5/4 because it is positive inside it must be negative then

$y = 5 {\left(x + \frac{1}{2}\right)}^{2} - 13.25$

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

the vertex is = $\left(- \frac{1}{2} , - 13.25\right)$