Question

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

Answer 1

as `xrarr-oo, f(x)rarr+oo` and
as `xrarr+oo, f(x)rarr+oo`

Explanation:

`f(x)=color(red)1x^color(blue)2-8x+18`

Because the degree `color(blue)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, `color(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 `xrarr-oo, f(x)rarr+oo` and
as `xrarr+oo, f(x)rarr+oo`