# What is the range of the function y=2x^2 +32x - 4?

Jan 17, 2018

$y \ge - 132$

#### Explanation:

This a quadratic function with positive leading coefficient so it has a minimum value at its vertex. The vertex of $y = a {x}^{2} + b x + c$ is $\left(h , k\right)$ where $h = - \frac{b}{2 a}$ and $k$ is found by substitution.

For the given function $h = - \frac{32}{2 \cdot 2} = - \frac{32}{4} = - 8$.

Find $k$ by substitution:

$k = 2 {\left(- 8\right)}^{2} + 32 \left(- 8\right) - 4$

$k = 128 - 256 - 4$
$k = - 132$

Since the minimum is $\left(- 8 , - 132\right)$ and there is no maximum value, the range of the function is $y \ge - 132$.