# How do you find the axis of symmetry, and the maximum or minimum value of the function f(x) = 2x^2 + x - 3?

May 20, 2017

Min $\left(- \frac{1}{4} , - \frac{25}{8}\right)$

#### Explanation:

$f \left(x\right) = 2 {x}^{2} + x - 3$
x- coordinate of axis of symmetry:
$x = - \frac{b}{2 a} = - \frac{1}{2} = - \frac{1}{4}$
Because a = 2 > 0, the parabola opens upward. There is a min.
To find the Min, replace x by (-1/4) in f(x).
$f \left(- \frac{1}{4}\right) = \frac{1}{8} - \frac{1}{4} - 3 = - \frac{1}{8} - 3 = - \frac{25}{8}$
Min $\left(- \frac{1}{4} , - \frac{25}{8}\right)$