Algebra 1 Common Core Student Edition, Grade 8-9

(Marvins-Underground-K-12) #1
Objective To solve systems of linear and quadratic equations

Hey, look at that!
Two equations with
tw o unknow ns— it
lo o k s lik e a s y s t e m ,
V ___

Two scooters leave a stoplight a t the
same tim e. T h e blue scooter accelerates
and then travels a t a constant speed, and
th e red scooter accelerates a t a constant
r a t e. T h e d is t a n c e d , in f e e t , e a c h
s c o o t e r t r a v e l s a f t e r t sec o n d s is sh o w n.
When does the red scooter catch up to
th e blue scooter? Explain.

d = 4 0 t

MATHEMATICAL
PRACTICES
Esse n t i a l U n d e r st a n d i n g You can solve systems of linear and quadratic
equations graphically and algebraically. This type of system can have two solutions, one
solution, or no solutions.

Systems of Linear and


Quadratic Equations


@ Common Core State Standards
A-REI.C.7 Solve a sim ple system consisting o f a linear
equation and a quadratic equation in tw o variables
algebraically and graphically... Also A-CED.A.3,
A-REI.D.11
MP 1, MP 3, MP 4, MP 5

Get t i n g Read y!

13

One solution No solutions

How can you solve
this system by
graphing?
The p o in ts w h e re th e tw o
graphs intersect are the
solutions of the system.

I S o l v i n g b y G r a p h i n g
What are the solutions of the system? Solve by graphing, y = x2 — x — 2

Step 1 Graph both equations in the same coordinate plane.
S te p 2 Identify the point(s) of intersection, if any. The points
of intersection are (-2 ,4 ) and (2, 0).

The solutions of the system are (-2 ,4 ) and (2, 0).

596 Ch ap t er 9 Qu ad r at i c Fu n ct i o n s an d Eq u at i o n s

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