13
Name:
Structures of Expressions
lr.,
Recdy, Se*, SoJ
fte*dy
Topic Standard form of a quadratic equation
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The standard form of a quadratic equation is defined
as
a, b, and c in the following equations.
Example: Given 4x2 + 7x 6, a = 4,b= 7, and c _6
y=ax2 *bx*c,(a*
Identify
-
t.y:5x2+3x*6
.)d
0=
U=L-
=
2. y =x2 -7x+3
IO
fu=
L-
e=
[=
Q=
Y:
x(x
)
A
I
10.y-(x+6)(x+6)
Y- Xl+ t)Y +3L
Y=?Xl-3xrl
o= L
b= '3
SECONDARY
II
//
77.
I
y= (x-3)2
Y,- x'-6 r+
I
b= l)c= aL
= ax2 +
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o
o
=--1{
L-
8.y=(x-1)(zx-1)
a= ___ I
,
D=
-,V
-L- ---- qI
I
u
in the form y
,=
a--
Q=
tt-
each product
- a)
): XLf
a=
6.y=8x2-Sx-2
-3x2 + 4x
.)
U =c= O
-5
Multiply and write
7.
a\
y:
d
A=
L-
5.
L-
t
n=-17-
4'Y:6x2-S
F
3.y=-2x2+3x
I
a=
3/
0).
_t\
*
bx + c. Then identify a, b, and c.
9.y:(Zx-Z)(3x+2)
,=
b=
7
1
- 1xa-1
O
c= -4
- =-(x*S)2
72.y
Y=-X\/o*-rt
q
a= -l
b= - lb
L-
q.J
-1<-
YW ffiffimathematics
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14
Structures of Expressions
Sef
Topie Graphing a standard Y = x2 parabola
13. Graph the eqtlation y = x2.
Include at least 3 accurate
G^rL rrqrquvrqt
a. Statethevertex of
'^ theparabola.
i^
{o.o
'rl.d
b. Comoletet he table of values for y =
r
f(x)
-3
1
-2
1
)
v2
-L
0
0
1
2
rf
3
7
Topic: Writing the'equation of a transformed parabola in vertex form.
Find a value for ro such that the graph
13.Y=x2+to
1 ct'rhpt'
I
AN1 ;Wf t'r.
L6. Y = -x2 +eo
2
(x-intercepts)
2 (x-interceptsJ
A^rr parJ,o *u^b-a
will have the specified number of x-intercepts.
15.
L4- Y =x2+to
1 (x-intercept)
bry
W:0
L7.
y: -x2'+ to
1 (x-intercept)
\):O
78.
2O.y:(x-t)2+t
Vertex? v;-/t ,a)
v".t"*r f+
SECONDARYII
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r
)
PosJ
t"
oru^h
*
Y=-x2+a
no (x-intercepts)
,
Grabh the following equations. State the vertex.
(Be accurate with your key points and shape!)
t9.y -(x-1)2
Y=x2+tr
no(x-intercepts)
2L
b.,/ *E*ol,* Nt)aher
Y
= 2(x-
Vertex?
ffi mathematics
TW ffi
vision project
15
Structures of Expressions 2.2
23.y
22.
=-(x+3)2-4
24.
y=-0.5(x+l)2++
LrilHf
l-il f l-l r
] ll
L
Ll
Lrl + +
lf
L
#
+
1 Eil
ti
t
rl
t#
l
I
/
Vertex?
^r
-\
l-5,O)
\-
Vertex?
Vertex?
rl
+
lr
{t.q)
\-/
So
Topic: Features of a parabola.
identify the vertex, the equation for the axis of symmetry (AoS), and state
the number of x-intercept(s)the parabola will have, if any. State whether the vertex will be
a minimum or a maxfmum.
Use the table to
25.
26.
28.
27.
-9
3
-6
-4 l3
-31-9
-2 I -29
-1 I -57
er!
a.
u"nu'r*,€sr
b. Aos: X: 2
b.
AoS:
c. x-int(s): e
c. x-int(s): O
c.
x-int(s):
,@r
d.
L) a.
a. vurrur(O
_7_.b.
AoS:
SECONDARYlI
x-o
MAX
vertex:
a>\
V
IMIN bT MAX
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-1,7
-24
-33
7) a.
X. -d
2
d. rrflN or@h
yw
-9
-L2
Vertex:
h
{- | t -s)
X.^7
c. x-int(s): o
b. Aos:
d. MrN o16-.]
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