How do you sketch the general shape of f(x)=-x^3+2x^2+1f(x)=−x3+2x2+1 using end behavior?

1 Answer
Marvin V.
Jun 25, 2017

The general shape is that of -x^3−x3

Explanation:

Since the first power is odd the general shape of the graph is similar to that of x^3x3. But we also need to take into account the negative so we say that it behaves like -x^3−x3. We can also find the y-intercept by replacing all the x-values with zeros:

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

y=1y=1

If the power is even then it would follow the general shape of x^2x2.

This is the graph of -x^3−x3
graph{-x^3 [-10, 10, -5, 5]}

This is the graph of f(x)=-x^3+2x^2+1f(x)=−x3+2x2+1
graph{-x^3+2x^2+1 [-10, 10, -5, 5]}

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