### Home > APCALC > Chapter 3 > Lesson 3.2.1 > Problem3-45

3-45.

At right is the graph of a function $f$ with tangent lines drawn at $x = −2, −1, 1,$ and $2$. $f ^\prime(0) = 0$. Use the slopes provided in the graph to write the slope function $f^\prime$. Also, write an equation for $f$. Homework Help ✎

First make a prediction about the shape of the slope graph. The original graph is a parabola. What will the slope graph look like?

Next, make a table showing $x$-values and their corresponding slopes. Be sure to include that when $x = 0$, the slope is $0$ (after all, look at the horizontal tangent line).

Use your table to find an equation of the slope function.