Algebra 1 Common Core Student Edition, Grade 8-9

Quadratic Functions

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

F- I F. C. 7 a Graph linear and quadratic functions and

show intercepts, maxima, and minima. Also A-CED.A.2,

F- I F. B. 4 , F- I F. C. 8 a , F- I F. C. 9

MP1, MP 2, MP 3, MP 4, MP 7

Objective To graph quadratic functions of the form y = ax2 + bx + c

Get t i n g Re ad y! «► x C

Be careful! T he
graph sh ow s th e
height of th e ball,
not th e path of
th e ball.

You throw a ball s tr a ig h t up into th e air and

ca tc h it a t th e same height you re le a se d it.

The parabola a t the right shows the height

h of th e ball in f e e t a f t e r t seconds. W hat

is th e to ta l d istan ce th e ball tra v e ls? For

how long does th e ball trav e l up? Explain your

reasoning.

-S.

|

T im e (s)

MATHEMATICAL

PRACTICESThe parabola in the Solve It has the equation h = —16?2 + 32f + 4. Unlike the

quadratic functions you saw in previous lessons, this function has a linear term, 327.

Esse n t i a l U n d e r st a n d i n g In the quadratic function y = a x 2 + bx + c, the

value of b affects the position of the axis of symmetry.

Consider the graphs of the following functions.

y = 2x2 + 2x 2x2 + 6x

1 y

(^1) i
1
I X
—I. \ 1^1 /o
1
1
X—
Notice that the axis of symmetry changes with each change in the b-value. The equation
of the axis of symmetry is related to the ratio §.
equation:
b
y = 2x2 + 2x
1=1 2 1
y = 2x2 + 4x
-=22 z
axis of symmetry: x = — ^ x= —1, or i —2^2
The equation of the axis of symmetry is x = — ^ ), or x zJo. 2 a^ '
y = 2x2 + 6x
1=3
x=~i
PowerAlgebra.com Lesso n 9- 2 Quadratic Functions 553