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

1 Answer
Jun 25, 2017

Answer:

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]}