Free Printable Alg 2 QR 3.1

Worksheets

Alg 2 QR 3.1 - 3.3

Total questions: 59

Worksheet time: 6hrs 34mins

Name

Class

Date

What is the first question you ask yourself when factoring a polynomial?

How many terms does it have?

Is there a GCF?

What strategy should I use?

Why do I have to learn this?!?!?!

Factor Completely:
3x² + 18x +15
Hint: Factor GCF first.

3(x² + 6x + 5)

(x + 5)(x + 1)

3(x + 5)(x + 1)

Prime

Factor
3a² + 4a + 1

(7a-10)(a-8)

Not factorable

(3a+1)(a+1)

(3a-1)(a-1)

Factor
k² - 2k - 24

(k+4)(k-6)

(k+4)(k+6)

(k+6)(k-1)

(k-4)(k+6)

Factor
3v² - 4v - 7

(3v-7)(v+1)

3(v-7)(v-1)

(3v+1)(v-9)

(3v+1)(v-10)

Factor out the GCF:
12x + 6

6(2x + 1)

3(4x + 2)

6x(2x + 1)

2(6x + 3)

What is the first step in solving
(x + 2)(x - 3) = 0 ?

Plug in zero for x

Solve for x

FOIL

Set each binomial factor equal to zero

What are the values of x when y = 0?

{ -3, 1 }

{ -2 }

{ -3, -1 }

{ 1, 3 }

Solve for the values of x:
(x - 3)(x + 6) = 0

{ -3, -6 }

{ 3, -6 }

{ -3, -6 }

{ 3, 6 }

10.

What are the x- intercepts?

(0, 0) and (-4, 0)

(0, 0) and (4, 0)

y= 0

x= 2

11.

3x² = 12

x = ± 2

x = 2

x = ± √12

x = ± 4

12.

x² + 4 = 68

x = ± 8

x = ± √8

x = 8

x = ± 64

13.

7x² + 1 = 8

x = ± 1

x = ± 7

x = ± √7

x = ± 8

14.

(x + 1) ² = 25

x = ± 5

x = 4 or -6

x = -4 or 6

x = ± 4

15.

16a² - 9 = 0

a = ^-3/₄, ³/₄

a = ^-4/₃, ⁴/₃

a = ^-9/₁₆, ⁹/₁₆

a = ^-16/₉, ¹⁶/₉

16.

5b² - 4 = 41

b = 9, b = -9

b = 3, b = -3

b = 8, b = -8

no solution

17.

5m² + 1 = 6

m = 0

m = 1 or -1

m = √7

m = 7/5 m = -7/5

18.

3 + 9r² = 12

r = 0

no solution

r = 3, r = -3

r = 1, r = -1

19.

x = ±72

x = ±12

x = 12

$x=\pm6i\sqrt[]{2}$

20.

4m² - 100 = 0

m=25, -25

m=96

m=5, -5

m=-96

21.

k² - 6 = 43

k = √37

k = 37 or - 37

k = 7, k = -7

no solution

22.

23.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

Set the equation equal to zero

Divide 10 by 2 and add the result to both sides

Add a² and 10a together

Subtract the 21

24.

What do you do to the b value to correctly complete the square?

square it

divide it by 2 and square the result

divide it by 2 and take the square root of the result

divide it by 2 only

25.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

26.

When do you use the plus or minus symbol?
±

After taking the square root of both sides

After adding the square to both sides

After taking half of b

After setting the equation equal to zero

27.

What is one of the solutions to this equation?
(2x - 1)² = 49

x = 7

x = -7

x = -4

x = -3

28.

Write the following quadratic expression in completed square form...

x² + 6x = 5

(x + 3)² = 5

(x + 6)² = 9

(x + 3)² = 14

(x + 6)² = 14

29.

Write the following quadratic expression in vertex form...

y = x² + 4x + 10

y = (x + 4)² + 6

y = (x + 2)² + 6

y = (x + 4)² - 6

y = (x + 2)² - 6

30.

Write the following quadratic expression in vertex form...

y = x² + 4x + 10

y = (x + 4)² + 6

y = (x + 2)² + 6

y = (x + 4)² - 6

y = (x + 2)² - 6

31.

Solve the following quadratics equation by completing the square...

x² - 10x - 5 = 0

x = -5 ± √30

x = 5 ± √30

x = 30 ± √5

x = -30 ± √5

32.

Solve the following quadratics equation by completing the square...

x² + 6x - 3 = 0

x = $-3\pm2\sqrt{3}$

x = $3\pm2\sqrt{3}$

x = $12\pm\sqrt{3}$

x = $-12\pm\sqrt{3}$

33.

Solve by completing the square.
x² +12x = 5

x = 6 + √41 or 6 − √41

x = 35 or 47

x = −6 + √41 or −6 − √41

x = √35 or √47

34.

The height of an object thrown into the air can be modeled by the formula h(t) = -16t² + 70t + 95, where h(t) is in feet after t seconds.
What is the height of the object after 5 seconds?

95 feet

45 feet

70 feet

171.56 feet

35.

What algebraic term are you solving for if the word problem is: The equation for leaping off a cliff is h = -16t² + 8t +24. How long will it take for you to hit the water?

Roots (Solutions)

Axis of Symmetry

Vertex

y-intercept

36.

A dolphin jumps from the water. The equation h = -16t² + 80t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

1 foot

5 feet

96 feet

100 feet

37.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t² + 64t + 80.
What will be the object's maximum height?

2 ft

80 ft

144 ft

64 ft

38.

What algebraic term are you solving for if the word problem is: The equation for leaping off a cliff is h = -16t² + 8t +24. How long will it take for you to hit the maximum height?

y coordinate of the vertex

Axis of Symmetry

x coordinate of the vertex

y-intercept

39.

What algebraic term are you solving for if the word problem is: Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec. This can be modeled with the function h(t) = -16t² + 96t. When does the rocket land?

x-intercept

y -intercept

vertex

axis of symmetry

40.

A ball is thrown vertically into the air. Its height in feet after t seconds is given by the equation h(t) = –5t² + 20t, and is graphed below. How high will the ball be after 3 seconds?

20 ft

15 ft

5 ft

10 ft

41.

Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec. This can be modeled with the function h(t) = -16t² + 96t. When does the rocket hit the ground?

7 seconds

6 seconds

3 seconds

8 seconds

42.

What does i² = ?

-1

√-1

-√1

43.

44.

45.

What is the simplified form of (-3 + 2i)(1- 4i)

-2 - 2i

5 + 14i

-11 -10i

-3 -8i

46.

What is the simplified form of (-6i)(3i)

-18

-18i

-18i²

47.

(3+4i)(-8-i)

-5+3i

-24-4i

-24-4i²

-20

-20-35i

48.

21 - 16i

21 -24i

11 - 16i

11 - 24i

49.

2 + 12i

-34 + 12i

34 + 12i

-2 + 12i

50.

8 + 14i

3 + 14i

13 + 14i

11 + 14i

51.

15i

9 + 6i

-3i

-9 + 6i

52.

What is the simplified form of (-9 + 5i) + (3 -2i)

-12 + 31i

-6 + 3i

-11 + 7i

5 - 3i

53.

What is the simplifies form of (11 - 7i) - (-3 + 12i)

8 - 19i

8 + 5i

13- 19i

14 -19i

54.

What is the simplified form of (8 -3i)²?

16 - 6i

55 + 48i

55 - 48i

55.

(5 - 2i) + (-7 + 8i)

-2+6i

12+6i

-35-16i²

-35 -16i

56.

(10 + 3i) - (2 - 9i)

20 - 27i

12 - 7i

8 + 12i

20 - 27i²

57.

(i)(3i)

-3i

-3

58.

Multiply
3i(-2 + 4i)

-6+12i

-12-6i

-2+7i

12+6i

59.

The product of (3 -2i) and (7+6i) is

21 - 12i

9 + 4i

33 + 4i

21 + 16i

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Alg 2 QR 3.1 - 3.3

Total questions: 59

Worksheet time: 6hrs 34mins

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