# How do you find the end behavior of x^3-4x^2+7?

Jul 14, 2018

End behavior : Down ( As $x \to - \infty , y \to - \infty$ ),
Up ( As
$x \to \infty , y \to \infty$),

#### Explanation:

${x}^{3} - 4 {x}^{2} + 7$. The end behavior of a graph describes far left

and far right portions. Using degree of polynomial and leading

coefficient we can determine the end behaviors. Here degree of

polynomial is $3$ (odd) and leading coefficient is $+$.

For odd degree and positive leading coefficient the graph goes

down as we go left in $3$ rd quadrant and goes up as we go

right in $1$ st quadrant.

End behavior : Down ( As $x \to - \infty , y \to - \infty$),

Up ( As $x \to \infty , y \to \infty$).

graph{x^3-4 x^2+7 [-20, 20, -10, 10]} [Ans]