ALGEBRA 1
Ch 8 Closure Quadratic Functions
(1) LOD L -ttiy
ONCEPTS:
1.
Name:
Factor completely.
a.
x 2 — 4x --12
x 2$), ---,
c.
x2
-6x+9
4V
e.
2
X ± 4x +1
-tY
h.
6x3 24x 2 +18x
H
_
..
••
•
••• '
2.
Equation —> Graph:
Without graphing, state everything you can about the graph given only the equation.
-a-,
-x+6
y = — x2
a.
ply-4 hi.D1 4._
x'
b.
6 i--_-..),,,,,i
r)
D IA cyl •)o/Ic_. 0-r- •-7L-1;Le......
- .,0,1,4_, 4,-- / e pA ,. is
,1 .'/L.4
y=(x+1)(x+5)
''''s-r) .
I•
- kev
.---1--)
y = (x -1) 2 - 9
c.
o)
4
1.9- e. 2 • (. -
(.),- _c
y-
V\ ,e
f
rp,.
,
,1,,_.,).
(
'I—Ai_
(- - .r) , D.) .
Eitl,d
. (,-,(1 top 10- oil'
>V_A‹
(4
4'1)
,
ft
\Ler -1---r.Ae- 11
1:1A 0-
3.
() ;
(,;171-
Equation
Table: Create a table for the given equations.
a.
2
y = —x
X
(
6
;)
)
C)
-2_
7-
-
x
- z
- 3
1-it
-
D
r
LI,
L'i
0
'-.1-
0
(-2)
td.
7_7
2-
-()'---c„
(t)
(v
+A'+
-1 -4.
-q -;
t t
..'"
b.
y=(x+1)(x+5)
x
o
-L
-7
-,
-S'
1 2-
5
0
- 3
y = (x -1) 2 - 9
x
- I
—
(-4)1D) (-3)()
C.
-2_
I
D.
0
(1)() (
(--1)(3)
L.)
v
-2-
-
0
--
(-“;---1
1
1
()1.-1
'-i-i
7-
0
- •S'
-1
-1
-g
()) 2 -1
-
Li'
5
5
0
-1
() 2-1
s.)7,--ai
-
-
6-0' -1
4.
a.
Table
Graph: Create a graph for the tables you created in #3.
y.,x2—x+6
b.
y=(.7c+1)(x+5)
y= (x —1) 2 —9
.0.5
trj
1,1‘
c.
0.5
5.
Graph —› Table: Use the graph below to generate a table.
6.
Table —> Equation: Use the table you created in #5 to identify the key points of the parabola,
then generate each type of equation listed.
1A,Ivfo
y-intercept:
(
Standard Form:
vertex:
(
GraphingNertex Form:
x-intercepts:
.
k—
)
(
f
d
)
Factored Form:
4.
/Alb-
e,„,te.e(
cdk, 5
bo
•
7.
Rewrite the following standard form equations in factored form.
a.
'Fx
:
-1H
2A.L-
b.
y = 3x 2 +2x-5
—72x2
3-
17
2.4
6, x
v„Ar,t,it,
4,)<
‘°i't,
)4,
14,4
8.
Rewrite the following standard form equations in graphing form by completing the square.
a.
y
+6x 7
b.
y
16
2
9.
Rewrite the following graphing form equations in standard form.
a.
y (x +1) 2 -4
b.
y = (x-2)2+7
-
ft
•
10.
Rewrite the following factored form equations in standard form.
a.
y=
(2x+ 5)(5x-2)
b.
y = 9(x 4-2)(x -2)
..1
-
0!
X
2-
x -71 0
0
11.
1,.
Calculate the x-intercept(s) and y-intercept and vertex for each equation. SHOW ALL WORK!
a.
y=x2+4x+3
-
b.
y
5x2 30x
(0) 7- 4 4.1 (0 ') 4- 5
0
7- 3
))4
0 -------
t ,,e._ 4- ) )
x_ 4-
-:: o
i
t )4.-+ 3 )
)e.'. 4- 3 ::
1
I
,
0
v
,
,
1
x-intercept(s):
E
y-intercept(s):
vertex:
?-"` (
!J f
(e.
(2 ):2- 4- f-(
0)
c.) ; 2.i
—)
2- . ', — 1
(-21
4 3
x-intercept(s):
0,
D)
y-intercept(s):
r)
vertex:
Ll"-C).)
D
11.
Calculate the x-intercept(s) and y-intercept and vertex for each equation. SHOW ALL WORK!
c.
Y=(2"-7)(x-7)
X -1=o
)(=---
(7.-• 0
6 — C.)
I
=
( )
i-21 -
(04-1)(0-7)
U
(-0 (-7)
(2, 9
(
V r_H-F--)/___
6).25 4-- i)( ,D,2 1; -
0
1) ( —71)
0,1s)
g 7_0
x-intercept(s):
o) ( 1 t 0)
y-intercept(s):
(D S w- j
11S)
x + 5) —25
(-5,-
D
y-intercept(s):
(D. 'ZS.
vertex:
x-intercept(s):
(
0 j
vertex:
y = —2(x-4) 2 AS 27,
f.
v
5
(-7
(L,
CO-
0
7
p
-2(X-- ti) 2
2_
Tit
•t
0
x-intercept(s):
x-intercept(s):
y-intercept(s):
y-intercept(s):
vertex:
vertex:
./k 4
O
__
.\)
+ 2-
VOCABULARY:
completing the square
difference of squares
factor
factored completely
Aaeterzeel.form.
generic rectangle
.122mateie--perfect square trinomial
Zero Product Property
9f. % (j-1'
vvk tr yl 1)-m 1 . et I
(
-eFte-x----stismktmet4er
•-•=inter-4eiat=r
V\ C)
ay-a_6 n
1.
This organizes x and y values into columns and rows.
2.
The story part of a problem is called this.
3.
This is what the answer is called when adding.
4.
This is what the answer is called when multiplying.
5.
This is a function that when graphed has horizontal segments that
are not continuous.
6.
A polynomial with only one term.
7.
A polynomial that has only two terms.
8.
An equation with a highest exponent of 2.
9.
When a quadratic equation is graphed, it creates this,
F
efry
c.747613LA.a_rj
/0.
10.
A parabola has this characteristic since a vertical line can be
drawn through the vertex and cuts the graph in half. A point on
one side of that vertical line can be reflected to the other side of
the line.
11.
This is where a graph crosses the x-axis. It is written as {x, 0) .
12.
This is where a graph crosses the y-axis. It is written as (0, y) .
13.
This is the lowest point or highest point on a parabola.
It is located on the line of symmetry.
14.
The form of a quadratic expression written like: y = x2 x - 2
15.
The form of a quadratic expression written like: y = (x
1)(x - 2)
2
The form of a quadratic expression written like: y = (x +1) -2
The values for x that make an equation true.
Ze-r-v.S
18.
This is another name for the solution of a quadratic expression.
It is usually found by using square roots.
19.
This is another name for solutions, roots, or x-intercepts.
To find these, set an equation equal to zero and solve for x.
VOCABULARY:
sir
grzephing.fecm.
-re.onztm4e4,-standard-form
diffar-giamicEsquafe,s,
„faetaf-
`,01P
uase4rifreFR4al
.L-p.r...o.duet_quadretiyc,eguatieR
s.rootl-
4aelemel4oilmQ.1849eFi&teetaiigle--
..symmetry
--y-intereept.
„zerosZ-44r4,4apedue-t-fapapaity
A diagram that helps you to multiply polynomials.
re-c-feum
J
...-vailaxterrf
-trrietiGn
J
E-b-7
21.
This is the direction given to reverse the distribution process.
When doing this on a quadratic expression, you would use the
"box" and "diamond".
Lc--51,,,A_pl_e4-e--1,--,
22.
This direction means you should look for a GCF first, then do a
"box" and "diamond" if possible.
23.
If two or more numbers are multiplied together and their product is
zero, then one of the numbers being multiplied has to be equal to
zero. This property is used to solve for x once a quadratic
expression is factored.
24.
An expression like y = 25x 2 -9 that when factored looks
like y = (5x + 3)(5x-3).
25.
An expression like
I
pe r
eat,f-{za-tre s
v.2).
-Jrr
+9 that when factored looks
like y = (x + 3)2 .
fr\A-144---Ca--e.
yk_
y = x 2 + 6x
26.
A process used to rewrite a quadratic expression from standard
form to graphing/vertex form.