Question

How do you sketch the general shape of `f(x)=-x^3+2x^2+1` using end behavior?

Answer 1

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`. We can also find the y-intercept by replacing all the x-values with zeros:

`f(0)=-(0)^3+2(0)^2+1`

`y=1`

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]}

This is the graph of `f(x)=-x^3+2x^2+1`
graph{-x^3+2x^2+1 [-10, 10, -5, 5]}