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

Dec 22, 2015

$\left(- \frac{5}{4} , \frac{71}{8}\right)$

#### Explanation:

The x-value of the vertex is found from the expression $- \frac{b}{2 a}$
$b = 5$ and $a = 2$ so $x = - \frac{5}{4}$
Substitute this into the original equation to get the y value of the vertex.
$y = 2 \cdot {\left(- \frac{5}{4}\right)}^{2} + 5 \cdot \left(- \frac{5}{4}\right) + 12$
$y = \frac{25}{8} - \frac{25}{4} + 12$
$y = \frac{25 - 50 + 96}{8} = \frac{71}{8}$
The vertex is $\left(- \frac{5}{4} , \frac{71}{8}\right)$