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Algebra: Concepts and Connections Quadratics Practice Assign.

Total questions: 70

Worksheet time: 4hrs 17mins

Name
Class
Date
1.

Does the function have a maximum or minimum?

a)

maximum

b)

minimum

c)
cannot be determined
2.
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
3.

Identify the 'b' value: y = 16x2 - 8x - 24

a)

16

b)

  • - 8

c)

8

d)

  • - 24

4.
What are the x- intercepts?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
5.

Which answer choice describes  y = -3x2 + 7x - 2 accurately?

a)
opens up with a maximum
b)
opens up with a minimum
c)
opens down with a maximum
d)
opens down with a minimum 
6.

What is the form of the quadratic function y = 2x2 - 6x + 1?

a)
Vertex Form
b)

Factored Form

c)
Standard Form 
d)
Cannot be determined
7.
.How many zeros does this parabola have? 
a)
3
b)
2
c)
0
d)
1
8.

What is the domain of f(x) = x² - 4?

a)

(−∞, ∞)

b)

 [-4, ∞)

c)

 [4, ∞)

d)

(∞, - ∞)

9.

Solve the equation. Hint: Graph the function to find the solutions.

a)
A
b)
B
c)
C
d)
D
10.

Solve the equation. Hint: Graph the function to find the solutions.

a)
A 
b)
B 
c)
C 
d)
D 
11.

Solve the equation. Hint: Graph the function to find the solutions.

a)
A 
b)
B 
c)
C 
d)
D 
12.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
13.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
14.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
15.

What shape is the graph of a quadratic?

a)

Hyperbola

b)

Parabola

c)

Straight Line

d)

Circle

16.

Parabolas can open which of the following ways?

a)

Up

b)

Down

c)

Right

d)

Left

17.

A parabola changes direction at what point?

a)

Slope

b)

Y-intercept

c)

vertex

d)

x-intercept

18.
What is the equation for the axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
19.
What is the green dot on the parabola called?
a)
maximum
b)
minumum
c)
roots
d)
zeros
20.
Find the y-intercept of f(x) = 2x2 - 2x + 1
a)
2
b)
-2
c)
1
d)
-1
21.
Does y = -4x2 have a maximum or minimum value?
a)
maximum
b)
minimum
22.
Determine the vertex of the parabola:
y = 5x2 - 20x + 13
a)
(5, -7)
b)
(-2, -7)
c)
(2, -7)
d)
(-7, -2)
23.
Which of the following is the correct equation for the given graph?
a)
f(x) = (x - 2)2 - 1
b)
f(x) = (x + 2)2 - 1
c)
f(x) = -(x + 2)2 - 1
d)
f(x) = -(x - 2)2 - 1
24.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
any random point
c)
vertex
d)
none of these
25.

What are the x - intercepts?

a)

x = 0 and x = -4

b)

x = 0 and x = 4

c)

y = 0

d)

x = 2

26.
Identify the vertex and whether the graph opens up or down.
a)
(-1, 4); opens up
b)
(-1, 4); opens down
c)
(1, 4); opens up
d)
(1, 4); opens down
27.

Factor x2 + 11x + 18

Hint: You could match up graphs if you have a hard time factoring.

a)

(x + 11)(x + 7)

b)

(x + 2)(x + 9)

c)

(x + 6)(x + 3)

d)

(x + 10)(x + 8)

28.

Factor: x2 - 7x + 10

Hint: You could match up graphs if you have a hard time factoring.

a)

(x - 5)(x - 2)

b)

(x + 5)(x + 2)

c)

(x - 5)(x + 2)

d)

(x + 5)(x - 2)

29.

What is the GCF of 5x2+20x

a)

5

b)

x

c)

5x

d)

20x

30.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
31.
Does this parabola have a maximum or minimum?
a)
Maximum
b)
Minimum
32.
What is the vertex for the equation y = ½(x - 4)² - 4?
a)
(- 4, - 4)
b)
(4, 4)
c)
(- 4, 4)
d)
(4, - 4)
33.

The height of a water balloon that is launched into the air is given by h(t) = -5t2 + 40t + 2. From what height was the balloon released?

a)

2 meters

b)

5 meters

c)

40 meters

d)

20 meters

34.

The height of a water balloon that is launched into the air is given by h(t) = -5t2 + 20t + 25. When will the balloon explode on the ground?

a)

5 seconds

b)

1 second

c)

2 seconds

d)

3 seconds

35.

Jason launched a rocket for a physics experiment. This equation can be used to find the height (h), in feet, of the rocket after t seconds.
h(t)=−16t2+288t+8h\left(t\right)=-16t^2+288t+8

How many seconds will it take for the rocket to reach a height of 1,304 feet?

a)

9.0 seconds

b)

9.6 seconds

c)

81.0 seconds

d)

82.0 seconds

36.

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t2 + 45

When is the ball at ground level?

a)

only at t = 0 seconds

b)

only at t = 3 seconds

c)

only at t = 9 seconds

d)

at both t = 0 seconds and t = 3 seconds

37.

If each mark on the x-axis represents one second, when did the object reach the ground?

a)

2.5 seconds

b)

6 seconds

c)

5.5 seconds

d)

5 seconds

38.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t2 + 40t + 10

How many seconds does it take the ball to reach its maximum height?

a)

1.25 seconds

b)

1.4 seconds

c)

2.5 seconds

d)

2 seconds

39.

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:

h = -16t2 + 80

About how long did it take for the balloon to hit the ground?

a)

1.73 seconds

b)

2.24 seconds

c)

2.45 seconds

d)

2.83 seconds

40.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x2 +600x +60

What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

41.

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?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

42.
Find the product:
(3x + 2)(2x + 4)
a)
6x2 + 16x + 8
b)
5x2 +11x + 6
c)
5x2 + 16x + 6
d)
6x2 + 11x + 8
43.
Multiply:
(3x – 1)(x + 5) 
a)
3x2 + 4x + 5
b)
3x2 + 4x - 5
c)
3x2 + 14x + 5
d)
3x2 + 14x - 5
44.
The graph of a quadratic function is called a
a)
Parabola
b)
Vertex
c)
Axis of Symmetry 
d)
Vertex Form
45.
What divides the parabola into 2 perfect halves?
a)
Axis of Symmetry
b)
Vertex
c)
Axis of Doom
d)
x - intercept
46.
What do we call the highest or lowest point of a quadratic?
a)
parabola
b)
vertex
c)
graph
d)
point
47.

The solutions to quadratic equations are known as......

a)

y-intercepts

b)

roots or zeros

c)

vertex

d)

axis of symmetry

48.
What is the vertex?
a)
(2, 4)
b)
(3, -1)
c)
(0, 8)
d)
(4, 2)
49.
What are the x- intercepts?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
50.

If given the equation

y = (x + 5)2 - 4,

what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(5, 4)

d)

(-5, 4)

51.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

52.
Which statement is correct?
a)
The maximum is 1
b)
The maximum is 6
c)
The minimum is -4
d)
The minimum is 6
53.

What is the vertex of the quadratic function?

a)

(0, 2)

b)

(2, 0)

c)

(8, 0)

d)

(3, 4)

54.

Is this a quadratic function?

y=2x+3x2−5y=2x+3x^2-5  

a)

Yes

b)

No

55.

What is the axis of symmetry?

a)

x = -1

b)

x = -2

c)

y = -1

d)

y = -2

56.
What are the x-intercepts?
a)
0 and 2
b)
-4 and 0
c)
2 and 3
d)
0 and 4
57.
Convert
 f(x) = 2(x - 2)2 +9
to standard form.
a)
f(x) = 2x2 + 8x + 9
b)
f(x) = 2x2 - 8x - 4
c)
f(x) = 2x2 - 8x + 17
d)
f(x) = 2x2 - 8x + 8
58.
Convert
 f(x) = -4(x - 1)2 +7
to standard form.
a)
f(x) = -4x2 + 3
b)
f(x) = -4x2 - 8x + 17
c)
f(x) = -4x2 +8x - 11
d)
f(x) = -4x2 +8x + 3
59.
x2 - 25
a)
( x + 5 ) ( x - 5 ) 
b)
( x - 5 ) ( x - 5 ) 
c)
( x + 5 ) ( x + 5 ) 
d)
Prime
60.
x2 - 16
a)
Prime
b)
( x - 4) ( x + 4) 
c)
( x - 8) ( x + 8) 
d)
( x - 4) ( x - 4) 
61.

4x2 - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)2

c)

(2x + 5)2

d)

2x + 5(2x - 5)

62.

Solve by factoring: x2 - 9x + 20 = 0
Hint: You could match up graphs if you have a hard time factoring.

a)
x = -4 and x = -5
b)
x = 20 and x = -9
c)
x = 4 and x = 5
d)
x = -4 and x = 5
63.

Solve by factoring: x2 + 3x - 18 = 0
Hint: You could match up graphs if you have a hard time factoring.

a)
x = -3 and x = 6
b)
x = 3 and x = -6
c)
x = -9 and x = 2
d)
x = 9 and x = -2
64.

Solve by taking square roots:

5b2 - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no real solution

65.

Use the quadratic formula to solve 2x2 + 2x - 12.

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

66.

Use the quadratic formula to find the solutions for

y = -x2 - 5x + 12

a)

No Real Solution

b)
c)
d)
67.

Solve the quadratic: n2 - 5 = -4

a)

n = ±√9

b)

n = ±3

c)

n = ±1

d)

No real solution

68.

k² - 2k = 0

Hint: You could match up graphs if you have a hard time factoring.

a)

k = 2 and 0

b)

k = -2 and 0

c)

k = 2

d)

k = 0

69.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
70.
Complete the square for
x2 + 12x + ____
a)
x2 + 12x + 144
b)
x2 + 12x + 36
c)
x2 + 12x - 36
d)
x2 + +12x - 144

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