Question

Two students in your class, Hunter and Maggie, are disputing a function. Hunter says that for the function, between x = −2 and x = 2, the average rate of change is 0. Maggie says that for the function, between x = −2 and x = 2, the graph goes up through a turning point, and then back down. Explain how Hunter and Maggie can both be correct, using complete sentences. (10 points)

Answer 1

Hunter and Maggie can both be correct because when the average rate of change is zero, the sum of all possible positive slopes and negative slopes on the interval will be zero. The sum of the possible positive slopes cancels out the sum of the possible negative slopes.

In this case the graph would be a parabola with the equation ax^2+bx+c where a is negative

Answer 2

According to hunter

In the interval [-2,2]

• The average rate of change is 0

According to Maggie

• The graph goes up through a turning point and back down

They can be correct

Because

If sum of all positive and negative slopes is zero then average rate of change is zeRos

So there is only one possibility

• It's a parabola
• The turning point is vertex

Then they both are correct