# What is the axis of symmetry and vertex for the graph y= 2x^2+7x-21?

Feb 2, 2018

$x = - \frac{7}{4} \text{ and } \left(- \frac{7}{4} , - \frac{217}{8}\right)$

#### Explanation:

$\text{given the equation of a parabola in standard form}$

•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0

$\text{then the x-coordinate of the vertex which is also the }$
$\text{equation of the axis of symmetry is}$

•color(white)(x)x_(color(red)"vertex")=-b/(2a)

$y = 2 {x}^{2} + 7 x - 21 \text{ is in standard form}$

$\text{with "a=2,b=7" and } c = - 21$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{7}{4}$

$\text{substitute this value into the equation for y}$

${y}_{\textcolor{red}{\text{vertex}}} = 2 {\left(- \frac{7}{4}\right)}^{2} + 7 \left(- \frac{7}{4}\right) - 21 = - \frac{217}{8}$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- \frac{7}{4} , - \frac{217}{8}\right)$

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