Algebra 2 — Unit 2 Day #4
Homework — Graphing Quadratic Functions
Name
Consider the equations y = 3 (x — 1) 2 — 5 and y = 3x2 — 6x — 2 .
a. Show algebraically that these two equations are equivalent.
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c)( 1 2)( 4-17 —
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toe +
3)( 1-
— 1.D)< —
b. Notice the value of "a" is 3 for both forms of the equation, but that the numbers for "b" and "c" are different
from the numbers "h" and "k'. Why do you think the value of "a" would be the same for both forms of the
equation?
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2. Use what you learned in the parabola investigation to write an equation for each of the parabolas described.
a. A parabola opening upward , shifted 8 units right and 5 units down.
7") b. A parabola with a stretch factor of 10, with its vertex sitting on the x-axis and line of symmetry at x = —6 .
oLx+ (4)2c. A downward opening parabola with vertex (-7, —2) and vertical compression of 0.6.
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X A-
3. Simplify the following:
+5f +2J
a. .1X +
‘.P
\C-ce
15-6
c.
4-
b. (2V10;1) :
375
a-5
13d. —
4
( e)
Algebra 2 — Unit 2 Day #4
Homework — Graphing Quadratic Functions
Name
C)
4. Given y = 8x 6 — 4x 5 — 106x 4 + 33x 3 + 346x 2 — 8x — 80
window —5 x 5, scale:1
—250 y 350, scale:50
a. What is the y-intercept?
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b. Identify all real roots to the nearest hundredth.
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X=
go)
x
c. Identify all relative maximums.
Are any of the values also an extrema?
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el
d. Identify all relative minimums
Are any of the values also an extrema?
b
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e. In what intervals is the graph positive?
f. In what intervals is the graph negative?
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-o5 c x c c 5
423-6 v c
g. In what intervals is the graph increasing?
(2,5i c x c 435
col c x c 1.59
2..(4
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h. In what intervals is the graph decreasing?
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1.51
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i. Describe the end behavior of the graph.
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(-2/o)
(- 2,
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Algebra 2 — Unit 2 Day #4
Homework — Graphing Quadratic Functions
Name
ThGraph each equation without using a table or your graphing calculator.
a. y = x 2 + 2
Vertex:
(0 1 "7-)
Orientation:
b. y
—3(x +
Vertex:
up
Stretch or Compression?
11
Orientation:
6) 2 +
of
H)
Compression?
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0 Lai
2
-12 .-10 •
2.4.6 • 9 • 10 •
............
6
8
12
1
c. y = 2x 2 — 10
d. y = -- (x — 4) 2 —
Vertex:
Orientation:
5
Vertex:
Orientation:
down
Compression?
Stretch o Compression?
12
10
8
2
/2 • 10
8
6
4
4
6 • 8 • 10 •
2. 10 • S
6 • .. • . 2 • - • 2 • 4 • 6 • 8 • 10 •
-4
N
If
12
-6
:108
-12
V
x
Algebra 2 - Unit 2 Day #4
Homework - Graphing Quadratic Functions
6. a. 3x 2 + 2x = 8
2-5< -2 r--0
discriminant
/00
# of x-intercepts
b. 4x 2
- 5x + 9
91 2-1 .5- )C+9
discriminant
°
/1
# of x-intercepts
a-
# of solutions
type of solution
Name
real_
Solve the following equations:
7. 64x 2 - 6 = 55
2
# of solutions
type of solution Ain
2 - 5=
( 3x + LO 2- 7-
8. -2(3x + 4
&the
)
r"--;0C tn
a 6) ti
45
tic
35(= ,-9 :E5M.
3"c+H
\I (dig
75
-
X•
3
x - H
9. 218x - 41 + 15 = 9
10.
I SY
3x- q-
)
5x
--
5%)(
-3=
as
3
- 71 = 10x -8
2_
-14)
p)5
y
Ax
1 -023
g/
- 5x Jr
II.
53.5 := 5.1-5