Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
2. Standard Form of a Quadratic Function
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Exercise 48 Page 207

Practice makes perfect
a We are given the two functions below. One is linear, and the other is a quadratic function.
We have to find the rate of change of each function from to Before starting the computations, let's remember the expression that gives us the rate of change of a function between and
Using this formula, we can find the rate of change of each of the given functions.
Rate of Change

From the table above, we conclude that the function has a greater rate of change from to We can also check it graphically.

Looking at the graph, we can say that both functions have the same change in the coordinates, but the change in the coordinates is greater for the function Therefore, has a greater rate of change.

b First, let's remember the formula to calculate the rate of change of a function from to
As in Part A, let's find the rate of change of each of the given functions from and
Rate of Change

From the table above, we conclude once more that the function has a greater rate of change from to We can also check it graphically.

Looking at the graph, we can say that both functions have the same change in coordinates, but the change in coordinates is greater for the function Therefore, has a greater rate of change.

c From the two previous results, and since the graph of is a line, we can affirm that the rate of change of is always constant and equal to However, the rate of change of is not constant, and it increases as increases.
We are interested in finding, if any, the values of and for which the expression above is greater than
Simplify
Let's analyze the inequality depending on the value of
  1. If it will depend on the value of to achieve this. For example, for and we will have but if then
  2. If then for all we will have

We conclude that must be greater than or equal to Therefore, the rate of change of is greater than for all