MATH 2201
QUADRATIC FUNCTIONS TEST REVIEW
1. Which of the following represents a quadratic function opening downwards?
(A) y = 3x2(x – 1)
(B) y = 3x(x – 1)
(C) y = – 3x2(x – 1)
(D)y = – 3x(x – 1)
2. Which graph does NOT represent a function?
(A)
(B)
(C)
(D)
3. Which is the y–intercept for the quadratic function y = x2 – 2x + 10?
(A) – 10
(B)
(C) – 2
10
(D)
2
4. Which quadratic function graphed below has a vertex at ( 2 , – 4 )?
(A)
(B)
(C)
(D)
5. What is the axis of symmetry for the quadratic function y = –2x2 – 8x – 5?
(A)
x=2
(B) x = – 2
(C)
x=4
(D) x = – 4
6. What is the domain and range of the quadratic function graphed?
(A) Domain: {x| – 1 ≤ x ≤ 3 ; xR}
(B) Domain: {x| – 1 ≤ x ≤ 3 ; xR}
(C) Domain: {x| xR}
(D) Domain: {x| xR}
Range:
Range:
Range:
Range:
{x| y ≥ – 8 ; yR}
{x| y ≤ – 8 ; yR}
{x| y ≤ – 8 ; yR}
{x| y ≥ – 8 ; yR}
7. Which statement is correct for the function graphed below?
(A) There is a maximum value of 3.
(C) There is a minimum value of 3.
(B) There is a maximum value of 2.
(D) There is a minimum value of 2.
8. Determine the equation of the axis of symmetry for the parabola that passes through
the points ( – 6 , 0 ) and ( 4 , 0 ).
(A) x = 2 (B) x = – 2 (C) x = 1 (D) x = –1
9. Which represents the quadratic function y = –2(x + 1)(x – 3) in standard form?
(A) y = –2x2 + 6
(C) y = –2x2 – 4x – 6
(B) y = –2x2 + 4x – 6
(D) y = –2x2 + 4x + 6
10. Which quadratic function opens downwards and has a vertex ( 0 , – 3 )?
(A) y = ( x + 3 )2
(B)
y = –( x + 3 )2
y = x2 – 3
(C)
(D)
y = –x2 – 3
11. What is the equation of the axis of symmetry for the function y = –4( x – 2 )2 + 3?
(A)
x=–2
(B)
x=2
(C)
(D) x = – 8
x=8
12. Which graph represents the function y = ( x + 4 )2 + 3?
(A)
(B)
(C)
(D)
(D)
13. Which quadratic function has a minimum value of 7?
(A)
y=
1
( x + 1 )2 + 7
2
(B)
y= 
1
( x + 1 )2 + 7
2
(C)
y=
1
( x + 1 )2 – 7
2
(D)
y= 
1
( x + 1 )2 – 7
2
14. Which quadratic function has zero x–intercepts?
(A)
y = 3( x + 4 )2 + 2
(B)
y = 3( x – 4 )2 – 2
(C)
y = –3( x + 4 )2 + 2
(D)
y = –3( x – 4 )2 + 2
15. Mark has 40 feet of lumber to enclose a rectangular flower garden. Which function
represents the area of the given flower garden, where x is the width of the garden?
(A) A(x) = –x2 + 40x
(B) A(x) = x2 + 40x
(C) A(x) = –x2 + 20x
(D) A(x) = x2 + 20x
x
x
16. Determine the following information from the graph.
y
2
-2
-2
-4
-6
-8
- 10
- 12
- 14
- 16
- 18
Equation of Axis of Symmetry:
2
4
6
x
Vertex:
Maximum or Minimum Value:
Y – intercept:
X – intercepts: ______
Domain:
Range:
17. Determine the quadratic function, of the parabola graphed below, in factored form.
y
14
12
10
8
6
4
2
-4
-2
-2
-4
2
4
6
x
18. A ball kicked into the air is represented by the function h(t) = –3t2 + 12t, where height, h, is given
in meters and time, t, is given in seconds. The path of the ball can be seen in the graph below.
h(t)
14
12
10
8
6
4
2
1
2
3
4
5
t
(a) What is the height of the ball at 3 seconds?
(b) What is the maximum height of the ball?
(c) When does the ball reach its maximum height?
(d) How long is the ball in the air?
(e) What is the domain and the range?
19. Given the function y = – 2x2 + 12x – 10 determine the following information and sketch the graph.
y
Equation of Axis of Symmetry: ___________
Vertex: __________
Maximum or Minimum value is __________
Number of x – intercepts:
Y–intercept:
Domain:
Range:
8
7
6
5
4
3
2
1
- 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1- 1
-2
-3
-4
-5
-6
-7
-8
-9
- 10
- 11
- 12
- 13
1 2 3 4 5 6 7 8
x
20.
Determine the following information and sketch the graph of the given function.
(a)
y=
1
( x – 2 )2 – 3
2
y
5
Direction of Opening:
4
3
Vertex:
2
1
Equation of the Axis of Symmetry:
-5 -4 -3 -2 -1
Maximum or Minimum Value:
-1
-2
-3
Number of x–intercepts:
-4
-5
Y–Intercept:
Domain:
Range:
21.
Determine the quadratic function, in vertex form, for the given graph.
1
2
3
4
5
x
22.
The trajectory of a rocket is represented by the function h(t) = – 4t2 + 16t + 20, where h is
height in meters and t is time in seconds.
(a) What is the initial height of the rocket before it takes flight?
(b) What is the height of the rocket after 3 seconds?
(c) At what time does the rocket reach its maximum height?
(d) What is the maximum height reached by the rocket?
23.
A storage space is to be constructed using 100 m of wire mesh fencing. If the warehouse is to
be used as one side of the storage space, what dimensions will produce a maximum area?
What is the maximum area of the storage space?
WAREHOUSE
24.
A travel agency offers a group rate of $2000 per person for a week in
Italy if 10 people sign up for the tour. For each additional person who
signs up, the price per person is reduced by $100.
(a) Determine the revenue function.
(b) Determine the maximum revenue that can be generated.
(c) What will be the new price per person be to generate the maximum revenue?
ANSWERS:
1. D
2. D
3. B
4. B
5. B
6. D
7.A
8.D
9. D
10. D 11. B 12. A
13. A 14. A 15. C
16. Axis of symmetry x = 2
Vertex (2 , –16)
Min = –16
Y – int = (0, –12)
x – ints = (–2, 0) and (16, 0)
Domain x є R
Range y ≥ –16
17. y = –2(x + 2)(x – 3)
18.(a) 9 m
(d) 4 sec
(b) 12 m
(c) 2 sec
(e) domain: 0 ≤ t ≤ 4
range: 0 ≤ h(t) ≤ 12
19. Axis of symmetry x = 3
Vertex (3 , 8)
Max = 8
Number of x – ints = 2
Y – int = (0, –10)
Domain x є R
Range y ≤ 8
y
5
4
20.
Direction: up
Vertex (2 , –3)
Axis of symmetry x = 2
Min = –3
Number of x – ints = 2
Y – int = (0, –1)
Domain x є R
Range y ≥ –3
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
21. y = –2(x + 2)2 + 6
22.(a) 20 m
(b) 32 m
23. 25 m x 50 m
(c) 2 sec
(d) 36 m
Area = 1250 m2
24.(a) R = –100x2 + 1000x + 20000 (b) $22 500
(c) $1500
1
2
3
4
5
x