# What is the axis of symmetry and vertex for the graph y = 2x^2 + 7x -5?

Feb 16, 2017

The axis of symmetry is $x = - \frac{7}{4}$
The vertex is $V = \left(- \frac{7}{4} , - \frac{89}{8}\right)$

#### Explanation:

In order to write the equation in the vertx form, we need to complete the squares

$y = 2 {x}^{2} + 7 x - 5$

$y = 2 \left({x}^{2} + \frac{7}{2} x\right) - 5$

$y = 2 \left({x}^{2} + \frac{7}{2} x + \textcolor{red}{\frac{49}{16}}\right) - 5 - \textcolor{b l u e}{\frac{49}{8}}$

$y = 2 {\left(x + \frac{7}{4}\right)}^{2} - \frac{89}{8}$

The axis of symmetry is $x = - \frac{7}{4}$

and the vertex is $V = \left(- \frac{7}{4} , - \frac{89}{8}\right)$

graph{(y-(2x^2+7x-5))(y-1000(x+7/4))=0 [-27.8, 23.5, -18.58, 7.1]}