Algebra 1 Common Core Student Edition, Grade 8-9

Objective To choose a linear, quadratic, or exponential model for data

Do you se e th e

pattern? You can

model it with a

fu n ction.

PRACTICES ^sser,t ial Underst anding You can use the linear, quadratic, or exponential

functions you have studied to model some sets of data.

Co n c ep t Su m m a r y Li near , Quad r at i c, and Exponent i al Funct i ons

Linear: y = mx + b Quadratic: y = ax2 + bx + c Exponential: y = a • lo*

Li n ear , Q u ad r at i c, an d

Ex p o n e n t i a l M o d e l s

Co m m o n Co r e St at e St a n d a r d s

F-LE.A.1a Prove that linear functions grow by equal

differences... and that exponential functions grow

by equal factors over equal intervals. Also F-LE.A.2,

F-LE.A.3

MP 1, MP 2, MP 3, MP 4, MP 7

Can you elim inate
possibilities?
Yes. For exam ple, you
k n o w th a t a lin e a r m odel
isn't appropriate in parts
(A) and (B) because the
slope between any tw o
p o in ts is n o t co n sta n t.

Pr o b l em 1 Ch o o si n g a M o d el b y Gr a p h i n g

Graph each set of points. Which model is most appropriate for each set?

Q (1,3), (0, 0), ( — 3, 3),

( - 1 , 1), ( 2, 0)

y

1

X

,0 i '

Quadratic model

0(0,2), (-1,4),

(1 ,1 ), (2, 0.5)

y

<

' 0

Exponential model

Q ( - 1 , — 2), (0, -1 ),

(1 ,0 ), (3 ,2 )

1 y

X

o.

Linear model

Lesson 9-7 Linear, Quadratic, and Exponential M odels^589