# How do you find the domain and range of M(x)= -2/14x^2-11x-15?

Apr 20, 2017

Find the Vertex.

#### Explanation:

This is a quadratic function, whose graph is a parabola.

First, find its vertex, $\left(h , k\right)$.

For $y = a {x}^{2} + b x + c$, the $x$-coordinate of the vertex is

$h = - \frac{b}{2 a .}$

In this case

$h = - \frac{11}{\frac{2}{7}} = - 11 \cdot \left(\frac{7}{2}\right) = - \frac{77}{2}$.

$k = M \left(h\right) = - \left(\frac{1}{7}\right) {\left(- \frac{77}{2}\right)}^{2} - 11 \left(- \frac{77}{2}\right) - 15 = \frac{787}{4}$

Since $a < 0$, the graph opens down.

The domain of every polynomial function is $\left(- \infty , \infty\right)$.
The range is $\left(- \infty , \frac{787}{4}\right]$.