Algebra 1 Common Core Student Edition, Grade 8-9

How can you get
started?
Begin by checking the
first differences o f the
y-values. Then check the
second differences and
ratios, if necessary.

& Got It? 1. Graph each set of points. Which model is most appropriate for each set?

a. (0, 0), (1,1), (-1, -0.5), (2, 3) b. (-2,11), (-1, 5), (0, 3), (1, 5)

When the x-values in a set of data pairs have a common difference, you can analyze

data numerically to find the best model. You can use a linear function to model data

pairs with y-values that have a common difference. You can use an exponential function

to model data pairs with y-values that have a common ratio.

no

+1

+1

+1

c

c

c

2 “ 1 ~>3

1 1 +' C

0 5 <

-------------------- J + 3

1 8 ^

+’ C

+' C

an

-2 0.25

-1 0.5

01

1 2

P*2

>2

5 *

The y-values have a common difference

of 3. A linear model fits the data.

For quadratic functions, the second

differences are constant.

In the table at the right, the second

differences of the y-values are all 4, so

a quadratic model fits the data.

The y-values have a common ratio of 2.

An exponential model fits the data.

Pr o b l em 2 Ch o o si n g a M o d el U si n g D i f f er e n ces o r Rat i o s

Which type of function best models the data? Use differences or ratios.

□

BUS

-0.25

-0.75

-1.25

-1.75

-0.5

The first differences are constant, so a

linear function models the data.

The second differences are constant, so a

quadratic function models the data.

Go t I t? 2. Which type of function best models the ordered pairs

(-1 , 0.5), (0,1), (1, 2), (2, 4), and (3, 8)? Use differences or ratios.

590 Chapter 9 Quadratic Functions and Equations