Free Printable Zero Product Property

1.

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

a)

(-5, 0) and (9, 0)

b)

(5,0) and (-9, 0)

c)

(5, 0) and (9, 0)

d)

(-3, 0) and (5, 0)and (-9, 0)

2.

What are the x-intercepts of the parabola?

y = ¼(x + 2)(x - 6)

a)

(-2, 0) and (6, 0)

b)

(2, 0) and (-6, 0)

c)

(-2, 6)

d)

(¼, 0) and (-2, 0) and (6, 0)

3.

True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

4.

Which quadratic equation models the parabola shown?

a)

y = (x-2)(x-5)

b)

y = (x+2)(x+5)

c)

y = -(x+2)(x+5)

d)

y = -(x-2)(x-5)

5.

Which quadratic equation models the parabola shown?

a)

y = (x-2)(x+5)

b)

y = (x+2)(x+5)

c)

y = -(x-2)(x-5)

d)

y = -(x+2)(x+5)

6.

What is the equation for this parabola in factored form?

a)

y=(x+2)(x-1)

b)

y=(x-2)(x+1)

c)

y=(x-2)(x-1)

d)

y=(x+2)(x+1)

7.

Which equation matches the x-intercepts x=5,-7 ?

a)

(x+5)(x-7)=0

b)

(x-5)(x+7)=0

c)

(x+5)(x+7)=0

d)

(x-5)(x-7)=0

8.

What are the x-intercepts:

(x - 5)(x - 1) = 0

a)

{ 5, 1 }

b)

{ 5, -1 }

c)

{ -5, 1 }

d)

{ -5, -1 }

9.

What are the x-intercepts:

(x - 3)(x + 6) = 0

a)

{ -3, -6 }

b)

{ 3, -6 }

c)

{ -3, -6 }

d)

{ 3, 6 }

10.

What are the zeros of the quadratic function below?

y = (2x – 5)(x + 6)

a)

–5/2, 6

b)

–6, 5/2

c)

5/2, 6

d)

–6, –5/2

11.

What are the zeros of the quadratic function shown in the graph?

a)

–2, –10

b)

–2, 10

c)

6

d)

2, 10

12.

Which of of the following is a linear factor for the quadratic function in the graph?

a)

x – 1

b)

x + 3

c)

x – 3

d)

x

13.

Which of the following is the graph of y = 0.5 (x – 8) (x + 2)?

a)

b)

c)

d)

14.

What are the zeros of the equation y = x(x + 5)?

a)

0, –5

b)

–5

c)

0, 5

d)

1, –5

15.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

16.

What are the x-intercepts?

a)

0 and 2

b)

-4 and 0

c)

2 and 3

d)

0 and 4

17.

What is the equation for this parabola in factored form?

a)

y=(x+2)(x-1)

b)

y=(x-2)(x+1)

c)

y=(x-2)(x-1)

d)

y=(x+2)(x+1)

18.

In factored form you can see the ______ of the graph easily.

a)

y-intercept

b)

vertex

c)

x-intercepts

19.

What is the factored quadratic equation in the following graph?

a)

( x+ 2)(x + 6) = y

b)

x² - 8x + 12 = y

c)

(x - 2)(x - 6) = y

d)

(x - 4)(x + 4) = y

20.

Find the zeros of this quadratic.

a)

b=4/5, b=3

b)

b=4, b=-3

c)

b=1/5, b=3

d)

b=4/5, b=-3

21.

What are the x-intercepts for g(x) = (x + 8)(x + 2)

a)

8 and 2

b)

(8, 2)

c)

-8 and - 2

d)

(-8, -2)

22.

What's another name for the x-intercepts?

a)

Roots

b)

Vertices

c)

axis of symmetry

d)

Minimums

23.

What are the zeros? y = (x - 3)(x + 8)

a)

-3 and 8

b)

3 and -8

c)

-3 and -8

d)

3 and 8

24.

Which of the following is Intercept (Factored) Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

25.

What is an equation of a quadratic with x-intercepts at $\left(-1,0\right)$ and $\left(-10,0\right)$

a)

$y=-2\left(x+1\right)\left(x-10\right)$

b)

$y=\frac{1}{3}\left(x+1\right)\left(x+10\right)$

c)

$y=-\frac{1}{10}\left(x-1\right)\left(x+10\right)$

d)

$y=3\left(x-1\right)\left(x-10\right)$

26.

What is an equation of a quadratic with x-intercepts at $\left(4,0\right)$ and $\left(-5,0\right)$

a)

$y=-\frac{1}{3}\left(x+4\right)\left(x-5\right)$

b)

$y=4\left(x+4\right)\left(x+5\right)$

c)

$y=-\frac{4}{5}\left(x-4\right)\left(x+5\right)$

d)

$y=3\left(x-4\right)\left(x-5\right)$

27.

What is an equation of a quadratic with x-intercepts at $\left(7,0\right)$ and $\left(11,0\right)$

a)

$y=-\frac{1}{3}\left(x+7\right)\left(x-11\right)$

b)

$y=-\left(x+7\right)\left(x+11\right)$

c)

$y=\frac{2}{5}\left(x-7\right)\left(x+11\right)$

d)

$y=\frac{3}{2}\left(x-7\right)\left(x-11\right)$

28.

$y=8\left(x-2\right)\left(x+3\right)$ What are the zeros (x-intercepts) of the equation

a)

$\left(2,0\right)\ and\ \left(3,0\right)$

b)

$\left(-2,0\right)\ and\ \left(3,0\right)$

c)

$\left(2,0\right)\ and\ \left(-3,0\right)$

d)

$\left(-2,0\right)\ and\ \left(-3,0\right)$

29.

$y=-\frac{2}{3}\left(x+1\right)\left(x+3\right)$ What are the zeros (x-intercepts) of the equation

a)

$\left(1,0\right)\ and\ \left(3,0\right)$

b)

$\left(-1,0\right)\ and\ \left(3,0\right)$

c)

$\left(1,0\right)\ and\ \left(-3,0\right)$

d)

$\left(-1,0\right)\ and\ \left(-3,0\right)$

30.

$y=\frac{1}{4}\left(x+5\right)\left(x-6\right)$ What are the zeros (x-intercepts) of the equation

a)

$\left(5,0\right)\ and\ \left(6,0\right)$

b)

$\left(-5,0\right)\ and\ \left(6,0\right)$

c)

$\left(5,0\right)\ and\ \left(-6,0\right)$

d)

$\left(-5,0\right)\ and\ \left(-6,0\right)$

31.

In which form is this equation? $y=(x-3)(x+8)$

a)

Standard

b)

Factored

c)

Vertex

d)

Parabolic

32.

Convert to Factored Form

x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

33.

Convert to Factored Form:

x² - 10x + 24

a)

(x - 6)(x - 4)

b)

(x + 6)(x + 4)

c)

(x - 12)(x + 2)

d)

(x - 8)(x - 3)

34.

Convert to Factored Form:

3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

35.

Convert to Factored Form

(hint...take out the greatest common factor first)

2c² + 2c - 84

a)

(c-6)(2c+14)

b)

(c+7)(2c-12)

c)

(c-4)(2c+21)

d)

2(c+7)(c-6)

36.

Convert to Factored Form:

(hint: use slide n' divide)

4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

37.

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

a)

(-5, 0) and (9, 0)

b)

(5,0) and (-9, 0)

c)

(5, 0) and (9, 0)

d)

(-3, 0) and (5, 0)and (-9, 0)

38.

What are the x-intercepts of the parabola?

y = ¼(x + 2)(x - 6)

a)

(-2, 0) and (6, 0)

b)

(2, 0) and (-6, 0)

c)

(-2, 6)

d)

(¼, 0) and (-2, 0) and (6, 0)

39.

Solve using Zero-Product Property.

(2x - 2)(5x + 5) = 0

a)

x = -1

b)

x = -1 or x = 1

c)

x = 1

d)

x = -2 or x = 5

40.

Which equation matches the x-intercepts x=5,-7 ?

a)

(x+5)(x-7)=0

b)

(x-5)(x+7)=0

c)

(x+5)(x+7)=0

d)

(x-5)(x-7)=0

41.

What are the x-intercepts:

(x - 5)(x - 1) = 0

a)

{ 5, 1 }

b)

{ 5, -1 }

c)

{ -5, 1 }

d)

{ -5, -1 }

42.

What are the x-intercepts:

(x - 3)(x + 6) = 0

a)

{ -3, -6 }

b)

{ 3, -6 }

c)

{ -3, -6 }

d)

{ 3, 6 }

43.

What does it mean to "find the zeros" of a quadratic?

a)

Plug in 0 and solve the expression.

b)

Factor then set each factor equal to zero and solve to find x-intercepts

c)

Set the expression equal to zero and solve

d)

Factor then set each factor equal to zero and solve to find y-intercepts

44.

The x-intercepts of a quadratic equation are known as the _____.

a)

vertices

b)

squares

c)

zeros

d)

formulas

45.

Solve for the values of x:

(x - 5)(x - 1) = 0

a)

(5, 0) or (1, 0)

b)

(-5, 0) or (-1, 0)

c)

(0, -5) or (0, -1)

d)

(0, 5) or (0, 1)

46.

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

a)

{ -3, -6 }

b)

{ 3, -6 }

c)

{ -3, -6 }

d)

{ 3, 6 }

47.

What are the solutions?

(2x + 5)(5x - 2) = 0

a)

x = -5/2, -2/5

b)

x = -5/2, 2/5

c)

x = 5/2, 2/5

d)

x = 5/2, -2/5

48.

What are the x-intercepts?

2(x + 5)(x + 1) = 0

a)

x = 0, 5, 1

b)

x = 0, - 5, -1

c)

x = 5, 1

d)

x = -5, -1

49.

In the equation
(x + 2)(x - 3) = 0, the binomials are called...?

a)

Factors

b)

Products

c)

Multiples

d)

Zeros

50.

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

a)

Plug in zero for x

b)

Solve for x

c)

FOIL

d)

Set each binomial factor equal to zero

51.

Solve for the values of x:
(x + 2)(x - 3) = 0

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

52.

Solve for the values of x:
(2x - 1)(x + 4) = 0

a)

{ 1/2, -4 }

b)

{ 1/2, 4 }

c)

{ 2, -4 }

d)

{ -2, 4 }

53.

Solve and find your x-intercepts:
0=x(x - 6)

a)

x=0 and x=-6

b)

x=1 and x=-6

c)

x=0 and x=6

d)

x=6

54.

Solve and find your zeros:
z(z - 15)=0

a)

z=0 and z=15

b)

z=0 and z=-15

c)

z=-15

d)

z=15

55.

What are the zeros of (2x+5)(x-6)=?

a)

-6, 5/2

b)

-5/2, 6

c)

6, 2

d)

5, -6

56.

Solve for X:

(x-5)(x+6)=0

a)

{5,5 }

b)

{ -5,-5 }

c)

{ -5,-6 }

d)

{5,-6 }

57.

Solve for x: x(x-3)(x-4) = 0

a)

{0,3,4 }

b)

{3,4 }

c)

{ 0,-3,-4 }

d)

{ }

58.

(4x+8)(8x-16)=0

a)

{2}

b)

{-2}

c)

{-2,2}

d)

{0,-2,2}

59.

Solve for x: (x - 7)(x + 2)

a)

-7, 2

b)

7, -2

c)

7, 2

d)

-7, -2

60.

Solve for x: (2x - 6)(x + 1)

a)

-6, 1

b)

3, -1

c)

-3, 1

d)

-3, -1

61.

$r\left(r+7\right)=0$

a)

$r=0,\ r=-7$

b)

$r=0,\ r=7$

c)

$r=-7$

d)

$r=7$

62.

$j\left(j-9\right)=0$

a)

$j=0,\ j=9$

b)

$j=0,\ j=-9$

c)

$j=9$

d)

$j=-9$

63.

$\left(u-2\right)\left(u+8\right)=0$

a)

$u=2,\ u=-8$

b)

$u=-2,\ u=8$

c)

$u=2,\ u=8$

d)

$u=-2,\ u=-8$

64.

$\left(7f-3\right)\left(9f+1\right)=0$

a)

$f=\frac{3}{7},\ f=-\frac{1}{9}$

b)

$f=-\frac{3}{7},\ f=\frac{1}{9}$

c)

$f=\frac{3}{7,}\ f=\frac{1}{9}$

d)

$f=-\frac{3}{7},\ f=-\frac{1}{9}$

65.

$\left(h+8\right)\left(h+5\right)=0$

a)

$h=-8,\ h=-5$

b)

$h=8,\ h=5$

c)

$h=-8,\ h=5$

d)

$h=8,\ h=-5$

66.

$\left(c+6\right)\left(c-7\right)=0$

a)

$c=-6,\ c=7$

b)

$c=6,\ c=-7$

c)

$c=6,\ c=7$

d)

$c=-6,\ c=-7$

67.

$\left(2q+1\right)\left(q-9\right)=0$

a)

$q=-\frac{1}{2},\ q=9$

b)

$q=\frac{1}{2},\ q=-9$

c)

$q=-\frac{1}{2},\ q=-9$

d)

$q=\frac{1}{2},\ q=9$

68.

$\left(h+8\right)\left(9h+7\right)=0$

a)

$h=-8.\ h=-\frac{7}{9}$

b)

$h=8,\ h=\frac{7}{9}$

c)

$h=-8,\ h=\frac{7}{9}$

d)

$h=8,\ h=-\frac{7}{9}$

69.

If the answer is ZERO, what must be true?

$xy=0$

a)

Both

x=0 and y=0

b)

Either

x=0 OR y=0

c)

x=2 and y=1/2

d)

x=2 and y= -1/2

70.

Solve for x

$5x=0$

a)

x=0

b)

x=5

c)

x=2

d)

x= -5

71.

Solve for x

x+5=0

a)

x=0

b)

x=5

c)

x=2

d)

x= -5

72.

Solve for x

$x-5=0$

a)

x=0

b)

x=5

c)

x=2

d)

x= -5

73.

Solve for x

$3x-6=0$

a)

x=0

b)

x=5

c)

x=2

d)

x= -5

74.

Use the Zero Product Property to solve for the values of x.

$\left(x+2\right)\left(x-3\right)=0$

a)

2 and 3

b)

-2 and -3

c)

2 and -3

d)

-2 and 3

75.

Solve using the Zero Product Property:
$\left(3x+2\right)\left(x+1\right)=0$

a)

$x=1,\ x=\frac{2}{3}$

b)

$x=-1,\ \ x=-\frac{2}{3}$

c)

$x=2,\ x=1$

d)

$x=-1,\ \ x=\frac{2}{3}$

76.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

77.

Solve for the values of x:

(2x - 1)(x + 4) = 0

a)

x = 1/2 or -4

b)

x = 1/2 or 4

c)

x = 2 or -4

d)

x = -2 or 4

78.

Solve for m

a)

m=1, m= -7

b)

m=0, m= -7

c)

m=0, m= 7

d)

m=-1, m= -7

79.

Solve for x

a)

x =8/3 or x =-3

b)

x=8/3 or x=3

c)

x= -8/3 or x=-3

d)

x= 3/8 or x=3

80.

Find the value for P

a)

p = 1/3 or p= -3/8

b)

p= 1/3 or p=3/8

c)

p= -1/3 or p=3/8

d)

p=3/1 or p=8/3

Zero Product Property

Total questions: 80

Worksheet time: 3hrs 36mins

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