Day 2:

Students should have tried to graph the original function given a linear rate of change… Intro will be spent going over homework talking about how to use linear ROC to produce the original (quadratic) function.

• Talk about once they “pull” the rate of change off of the ROC graph, they would use that rate over whatever next interval they choose
• This will take a lot of demonstration… odds are if they try it at home, odds are it will be wrong… so this will take practice…
• Once you clarify, maybe have them try (those who didn’t already, and compare with a neighbor)
• Have a couple pairs maybe come put their graphs up (to get the “choppy” curve we expect
• Show Carlos’ graph to talk about how if you take these rates of change at smaller intervals

In Class Discussion:

Given a quadratic find the rate of change over given intervals:

• Demo what they’re expected to do
• Possibly have them graph the rate of change vs x (right hand or left hand)

In Class Activity

Use the following graph to find a relationship for the rate of change over interval size 1.

Do this for x values -4 to 4.

Point 1

Point 2

Rate of change between them

1)

2) Graph the rate of change on the y-axis for each corresponding x value from the far left column

3) What do you notice about the rate of change for the original function? (Hint: Look at the graph from number 2)

4) Write an equation for the graph in number 2.

5) What if we took an interval size of 2? Would the graph behave in the same way as interval size 1?

6) What if we took an interval size of ½? Would the graph behave in the same was as the previous? Why?

Homework

For each of the following

a) Make a table of values for the rate of change between various points

b) Then GRAPH the rate of change on the y-axis for each corresponding x-value in the left column

1)

Point 1

Point 2

Rate of change between them

2)

Point 1

Point 2

Rate of change between them

3)

Point 1

Point 2

Rate of change between them

4)

Point 1

Point 2

Rate of change between them