# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=2x^2+x-21?

Jul 16, 2018

The axis of symmetry is $x = - \frac{1}{4}$. The minimum value is at $\left(- \frac{1}{4} , - 21.625\right)$

#### Explanation:

The axis of symmetry of the function

$f \left(x\right) = a {x}^{2} + b x + c$

is

$x = - \frac{b}{2} a$

The function is

$y = 2 {x}^{2} + x - 21$

$a = 2$

$b = 1$

Therefore,

The axis of symmetry is

$x = - \frac{1}{2 + 2} = - \frac{1}{4}$

The minimum value is

$f \left(- \frac{1}{4}\right) = 2 \cdot {\left(- \frac{1}{4}\right)}^{2} - \frac{1}{4} - 21 = \frac{1}{8} - \frac{1}{4} - 21 = - 21.125$

The minimum value is at $\left(- \frac{1}{4} , - 21.625\right)$

The graph is as following

graph{2x^2+x-21 [-45.93, 58.1, -34.35, 17.7]}