Download Teacher: Ms. Williams Name: 1. Factor: x2 − x − 6 1. (x − 3) (x + 2) 2

3/18/13
POW #16 - 2013
Teacher: Ms. Williams
Name: ____________________________________
1.
4.
Factor: x 2 − x − 6
Factor: x 2 + 5x
1.
2.
3.
4.
(x
(x
(x
(x
− 3) (x
+ 3) (x
− 1) (x
− 6) (x
+ 2)
− 2)
− 6)
− 1)
1.
2.
3.
4.
x(x + 5)
5(x + 1)
x
x+5
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2.
5.
Factor: y2 - 100
Factor: x 2 + 6x + 8
1.
2.
3.
4.
( y - 10)2
( y - 10)( y - 10)
( y + 10)( y + 10)
( y + 10)( y - 10)
1.
2.
3.
4.
(x
(x
(x
(x
+ 2)(x + 4)
- 2)(x - 4)
- 2)(x + 4)
+ 2)(x - 4)
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3.
6.
Express x 2 - 5x - 24 as the product of two binomials.
Express 9 - y2 as the product of two binomial factors.
1.
2.
3.
4.
(x
(x
(x
(x
- 8)(x + 3)
+ 8)(x - 3)
+ 6)(x + 4)
- 6)(x - 4)
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1.
2.
3.
4.
(3 + y)(3 - y)
( y + 3)(y - 3)
(3 - y)(3 - y)
( y + 3)( y + 3)
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7.
10.
Factor: x 2 - 4x - 5
How many solutions are there to the following system of
equations:
1.
2.
3.
4.
(x
(x
(x
(x
+ 5)(x + 1)
+ 5)(x - 1)
- 5)(x + 1)
- 5)(x - 1)
--------------
8.
Which is a factor of x 2 + 5x - 24?
1. (x + 4)
2. (x - 4)
3. (x + 3)
4. (x - 3)
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9.
Factor completely: 2a2 + 2a - 84
1.
2.
3.
4.
(2a - 7)(a + 6)
2(a - 7)(a - 6)
2(a - 7)(a + 6)
2(a + 7)(a - 6)
--------------
y=6-x
y = x 2 - 6x + 6
1.
2.
3.
4.
5.
1
2
3
4
0
--------------
11.
Factor completely: 2x 2 - 50
1.
2.
3.
4.
(x + 5)(2x - 5)
(2x + 5)(x - 5)
2(x - 5)2
2(x + 5)(x - 5)
--------------
12.
Factor completely: 2x 2 - 18
1.
2.
3.
4.
2(x
2(x
2(x
2(x
- 3)2
+ 3)2
+ 3)(x - 3)
+ 9)(x - 9)
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13.
16.
Solve the following system of equations algebraically
and check:
Factor completely: 3x 2 + 15x - 42
y = x 2 + 2x - 4
y - 5 = 2x
The solution with a positive value for y is (
,
1.
2.
3.
4.
3(x 2 + 5x - 14)
3(x - 7)(x + 2)
3(x + 7)(x - 2)
3(x + 14)(x - 1)
--------------
).
17.
The solution with a negative value for y is (
,
Solve the following system of equations:
).
y = x 2 + 4x + 1
y = 5x + 3
--------------
14.
What are the factors of y3 - 4y?
1. (1,2) and (2,13)
3. (-1,-2) and (2,13)
2. (-1,-2) and (-2,13)
4. (-1,-2) and (-2,-13)
--------------
1.
2.
3.
4.
y(y - 2)(y - 2)
y(y + 4)(y - 4)
(y2 + 1)(y - 4)
y(y + 2)(y - 2)
--------------
18.
Which is an equation of the line of symmetry for the
parabola in the accompanying diagram?
15.
What are the factors of x 2 - 10x - 24?
1.
2.
3.
4.
(x
(x
(x
(x
- 4)(x + 6)
- 4)(x - 6)
- 12)(x + 2)
+ 12)(x - 2)
--------------
1. x = 2
2. x = 4
3. x = 3
4. y = 3
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19.
23.
Find the axis of symmetry for the quadratic equation y = Find the vertex for the quadratic equation and tell if the
vertex is a maximum or a minimum: y = -(x + 2)2 - 4.
−x 2 − 8x + 10.
1. (1, -4), maximum
3. (2, -4), minimum
2. (-2, -4), maximum
Answer: x =
4. (-1, 2), minimum
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--------------
24.
20.
Find the turning point and the axis of symmetry for the
quadratic equation y = x 2 − 4x + 8.
1. (2, 4) and y = 2
2. (2, 4) and x = 2
3. (4, 8) and x = 4
4. (−2, 20) and x = −2
--------------
21.
Find the turning point for the quadratic equation, y =
3x 2 + 6x - 2, and tell whether the point is a maximum
or a minimum point.
1. (1, 5) and a minimum
3. (-1, -5) and a
minimum
2. (-1, -5) and a
4. (-1, 5) and a
maximum
maximum
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22.
Find the vertex for the quadratic equation, y = -4x 2 4x + 1, and tell whether the point is a maximum or a
minimum point.
1. (0.5, -4) and a
3. (0.5, 4) and a
minimum
minimum
2. (-0.5, -1) and a
4. (-0.5, 2) and a
maximum
maximum
Solve the following system of equations algebraically.
y = x 2 − 4x − 1
y=x−7
1.
2.
3.
4.
(2, −5), only
(2, −5) and (3, −4)
(3, −4), only
(−2, −9) and (3, −4)
--------------
25.
Solve the following system of equations algebraically.
y = x2 + x − 2
y = 1 + 3x
1.
2.
3.
4.
(−1, −2), only
(2, 7) and (−3, 4)
(−3, −8)
(3, 10) and (−1, −2)
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26.
29.
Solve the following system of equations algebraically.
What are the vertex and the axis of symmetry of the
parabola shown in the diagram below?
y = x 2 + 2x
y = 2x + 4
1.
2.
3.
4.
(−2, 8), only
(−2, 0) and (2, 8)
(2, 8), only
(2, −8) and (−2, 8)
--------------
27.
Graphically find the roots of the equation y = x 2 + 4x −
32.
1.
2.
3.
4.
x
x
x
x
= −8, only
= 8 and −4
= −8 and 4
= −8 and −4
--------------
28.
1. The vertex is (-2,-3), and the axis of symmetry is
x = -2.
2. The vertex is (-2,-3), and the axis of symmetry is
y = -2.
3. The vertex is (-3,-2), and the axis of symmetry is
y = -2.
4. The vertex is (-3,-2), and the axis of symmetry is
x = -2.
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The expression x 2 −
1.
2.
3.
4.
(x
(x
(x
(x
+ 2)(x
− 2)(x
+ 4)(x
+ 8)(x
16 is equivalent to
− 8)
+ 8)
− 4)
− 8)
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30.
32.
Consider the graph of the equation y = ax 2 + bx + c,
when a ≠ 0. If a is multiplied by 3, what is true of the
graph of the resulting parabola?
1. The vertex is 3 units above the vertex of the
original parabola.
2. The new parabola is 3 units to the right of the
original parabola.
3. The new parabola is wider than the original
parabola.
4. The new parabola is narrower than the original
parabola.
The expression 9x 2 – 100 is equivalent to
1. (9x – 10)(x + 10)
2. (3x – 10)(3x + 10)
3. (3x – 100)(3x – 1)
4. (9x – 100)(x + 1)
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31.
A swim team member performs a dive from a 14-foothigh springboard. The parabola below shows the path
of her dive.
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33.
What are the vertex and axis of symmetry of the
parabola y = x 2 − 16x + 63?
1.
2.
3.
4.
vertex: (8,−1); axis of symmetry: x = 8
vertex: (8,1); axis of symmetry: x = 8
vertex: (−8,−1); axis of symmetry: x = −8
vertex: (−8,1); axis of symmetry: x = −8
--------------
Which equation represents the axis of symmetry?
1. x = 3
3. x = 23
2. y = 3
4. y = 23
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34.
35.
The equation y = x 2 + 3x − 18 is graphed on the set of The equation y = −x 2 − 2x + 8 is graphed on the set of
axes below.
axes below.
Based on this graph, what are the roots of the equation Based on this graph, what are the roots of the equation
−x 2 − 2x + 8 = 0?
x 2 + 3x − 18 = 0?
1. 8 and 0
3. 9 and −1
1. −3 and 6
3. 3 and −6
2. 2 and −4
4. 4 and −2
2. 0 and −18
4. 3 and −18
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36.
Find algebraically the equation of the axis of symmetry
and the coordinates of the vertex of the parabola whose
equation is y = −2x 2 − 8x + 3.
Equation of the AOS: x =
Coordinates of the vertex: (
,
)
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37.
39.
What is the equation of the axis of symmetry of the
parabola shown in the diagram below?
The height, y, of a ball tossed into the air can be
represented by the equation y = −x 2 + 10x + 3, where
x is the elapsed time. What is the equation of the axis of
symmetry of this parabola?
1. y = 5
3. x = 5
2. y = −5
4. x = −5
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40.
A student correctly graphed the parabola shown below
to solve a given quadratic equation.
1. x = −0.5
2. x = 2
3. x = 4.5
4. x = 13
--------------
38.
If Ann correctly factors an expression that is the
difference of two perfect squares, her factors could be:
1.
2.
3.
4.
(2x + y)(x − 2y)
(2x + 3y)(2x − 3y)
(x − 4)(x − 4)
(2y − 5)(y − 5)
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What are the roots of the quadratic equation
associated with this graph?
1.
2.
3.
4.
−6 and 3
−6 and 0
−3 and 2
−2 and 3
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POW #16 - 2013
41.
45.
The expression x 2 − 36y2 is equivalent to
State the equation of the axis of symmetry and the
coordinates of the vertex of the parabola graphed
below.
1.
2.
3.
4.
(x
(x
(x
(x
− 6y)(x − 6y)
− 18y)(x − 18y)
+ 6y)(x − 6y)
+ 18y)(x − 18y)
--------------
42.
What are the factors of the expression x 2 + x − 20?
1.
2.
3.
4.
(x
(x
(x
(x
+ 5) and (x
+ 5) and (x
− 5) and (x
− 5) and (x
+ 4)
− 4)
+ 4)
− 4)
--------------
43.
1.
2.
3.
4.
AOS: x = 1; vertex (1, −5)
AOS: y = 1; vertex (1, −5)
AOS: x = 1; vertex (1, 5)
AOS: x = 1; vertex (−1, −5)
--------------
Which ordered pair is a solution of the system of
equations y = x + 3 and y = x 2 − x?
1. (6,9)
3. (3,−1)
2. (3,6)
4. (2,5)
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44.
The area of a rectangle is represented by x 2 − 5x − 24.
If the width of the rectangle is represented by x − 8,
express the length of the rectangle as a binomial.
1. x – 3
3. x + 3
2. x – 16
4. x + 32
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46.
48.
What are the vertex and the axis of symmetry of the
parabola shown in the graph below?
The equation of the axis of symmetry of the graph y =
2x 2 – 3x + 7 is
1. x =
2. y =
3. x =
4. y =
--------------
1.
2.
3.
4.
vertex: (1,6); axis of symmetry: y = 1
vertex: (1,6); axis of symmetry: x = 1
vertex: (6,1); axis of symmetry: y = 1
vertex: (6,1); axis of symmetry: x = 1
49.
What is the vertex of the parabola represented by the
equation y = –2x 2 + 24x – 100?
--------------
47.
1. x = –6
3. (6, –28)
2. x = 6
4. (–6, –316)
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Which expression is equivalent to 64 – x 2?
1.
2.
3.
4.
(8 – x)(8 – x)
(8 – x)(8 + x)
(x – 8)(x – 8)
(x – 8)(x + 8)
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50.
The graph of a parabola is represented by the equation
y = ax 2 where a is a positive integer. If a is multiplied
by 2, the new parabola will become
1.
2.
3.
4.
narrower and open downward
narrower and open upward
wider and open downward
wider and open upward
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