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Copyright © by Holt, Rinehart and Winston. 30 Holt Algebra 1All rights reserved.
Name Date Class
ReteachLinear, Quadratic, and Exponential Models11-4
LESSON
Graph to decide whether data is best modeled by a linear, quadratic or exponential function.
Graph ! !2, 0 " , ! !1, !3 " , ! 0, !4 " , ! 1, !3 " , ! 2, 0 " . What kind of model best describes the data?
Graph each data set. Which kind of model best describes the data?
1. ! !2, !4 " , ! !1, !2 " , ! 0, 0 " , ! 1, 2 " , ! 2, 4 " 2. ! !1, 4 " , ! 0, 2 " , ! 1, 1 " , ! 2, 1 __ 2 " , ! 3, 1 __ 4 "
linear exponential
Look for a pattern in each data set to determine which kind of model best describes the data.
3. x y
0 6
1 12
2 24
3 48
4. x y
0 10
1 18
2 28
3 40
5. x y
3 4
6 !2
9 !8
12 !14
exponential quadratic linear
You can also look at patterns in data to determine the correct model.
Linear functions have constant 1st differences.
x y
2 5
4 2
6 !1
8 !4
Quadratic functions have constant 2nd differences.
x y
1 !8
2 !5
3 0
4 7
Exponential functions have a constant ratio.
x y
0 !2
1 !8
2 !32
3 !128
Connect the points.The data appear to be quadratic.
!3
!3
!3
"3
"5
"7
"2
"2
#4
#4
#4
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12.03 Notes - compare functions
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Copyright © by Holt, Rinehart and Winston. 34 Holt Algebra 1All rights reserved.
Name Date Class
LESSON
Use the table below to help you learn the characteristics of each data model and how to tell them apart.
Model Linear Quadratic Exponential
Pattern(y-values)
constant first differences
constant second differences
constant ratios
Graph
Equation y ! mx " b y ! ax 2 " bx " c y ! a b x
Identify each of the following as linear, quadratic, or exponential.
1. y ! 6 ! 2 " x 2. y ! 4x " 6 3. y ! 2 x 2 " 5x " 3
exponential linear quadratic
4. 5. 6.
quadratic exponential linear
7. 8. 9.
linear quadratic exponential
11-4Reading StrategiesUse a Table
x 5 4 3 2 1
y 128 64 32 16 8x #6 #7 #8 #9 #10
y 17 20 23 26 29
x 1 3 5 7 9
y 4 12 28 52 84
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