# How do you describe the end behavior for f(x)=-x^2-8x-15?

Jan 13, 2018

See below.

#### Explanation:

For end behaviour of a polynomial, we only have to look at the leading coefficient and degree. In this case:

$- {x}^{2}$

as $x \to - \infty$ , $\textcolor{w h i t e}{888} - {x}^{2} \to - \infty$

as $x \to \infty$ , $\textcolor{w h i t e}{888} - {x}^{2} \to - \infty$

${x}^{2} > 0 \textcolor{w h i t e}{888}$ for all $\mathbb{R} \textcolor{w h i t e}{888}$, so $\textcolor{w h i t e}{8} - {x}^{2} < 0$ for all $\mathbb{R}$

Since the coefficient of ${x}^{2} < 0$, the parabola is of the form:

$\bigcap$

GRAPH:

graph{y=-x^2-8x-15 [-10, 5, -5, 4]}