# How do you describe the end behavior of f(x)=x^2-8x+18?

Sep 29, 2016

as $x \rightarrow - \infty , f \left(x\right) \rightarrow + \infty$ and
as $x \rightarrow + \infty , f \left(x\right) \rightarrow + \infty$

#### Explanation:

$f \left(x\right) = \textcolor{red}{1} {x}^{\textcolor{b l u e}{2}} - 8 x + 18$

Because the degree $\textcolor{b l u e}{2}$ is even, this an even function. Even functions have end behaviors that both go in the same direction in y.

The function has a positive leading coefficient, $\textcolor{red}{1}$. Even functions with positive leading coefficients have end behaviors that both go toward positive infinity (both ends of this quadratic/parabola graph point "up").

In other words,

as $x \rightarrow - \infty , f \left(x\right) \rightarrow + \infty$ and
as $x \rightarrow + \infty , f \left(x\right) \rightarrow + \infty$