# How do you sketch the general shape of f(x)=-x^3+4x^2-7 using end behavior?

Jun 25, 2017

The general shape is that of $- {x}^{3}$

#### Explanation:

Since the first power is odd the general shape of the graph is similar to that of ${x}^{3}$. But we also need to take into account the negative so we say that it behaves like $- {x}^{3}$.

If the power is even then it would follow the general shape of ${x}^{2}$.

This is the graph of $- {x}^{3}$
graph{-x^3 [-10, 10, -5, 5]}

And this is the graph of $f \left(x\right) = - {x}^{3} + 4 {x}^{2} - 7$
graph{-x^3+4x^2-7 [-22.8, 22.8, -11.4, 11.4]}