Mathematics 521A: EXAM REVIEW [Ch. 7]
Multiple Choice
Identify the choice that best completes the statement or
answers the question.
1. Which relation is quadratic?
A. y = x2 – x2 + 4x + 2
B. y = (2x2)(x + 1)
2
C. y = (x + 5)
D. y = 2x – 6x + 3
6. The points (–2, 4) and (1, 4) are located on the same
parabola. What is the equation for the axis of
symmetry for this parabola?
A. x = –0.5 B. x = –1 C. x = 0.5 D. x = –1.5
7. Solve x2 + 5x + 4 = 0 by factoring.
2. What is the degree of a quadratic function?
A. 3
B. 2
C. 0
A. x = –5 or x = –1 B. x = 5 or x = 1
C. x = 4 or x = 1
D. x = –4 or x = –1
D. 1
3. What is the y-intercept for y = 3x2 + 2x – 5?
A. –5
B. 5
C. 2
8. Solve w2 – 10w – 24 = 0 by factoring.
A. w = –8 or w = –3 B. w = –2 or w = 12
C. w = 2 or w = –12 D. w = –6 or w = –4
D. 3
4. Which parabola opens upward?
9. Solve 6x2 + 13x – 5 = 0 by factoring.
A. y = 2x – 4x – 5 B. y = 2 + 4x – 5x
C. y = 4 – 2x2 –5x D. y = –5x + 4x2 + 2
2
2
A. x = –2 or x = 3
C. x =
or x = –
B. x = 2 or x = –3
D. x = –
or x =
5. Which set of data is correct for this graph?
y
10. Solve 2x2 + 11x + 12 = 0 by factoring.
3
2
A. x =
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
or x = 4
B. x = 4 or x = 3
C. x = –4 or x = –3 D. x = –
x
or x = –4
–2
–3
11. Solve 4p2 + 15p = –9 by factoring.
–4
–5
Set
A.
B.
C.
D.
A of S
x = –2
x = –6
x = –2
x=2
A. Set A.
–6
A. p = –
–7
C. p = –4 or p = 3
Vertex
(–2, 6)
(–6, –2)
(–2, –6)
(2, 6)
B. Set B.
Domain
xR
–8  x  4
xR
–6  x  2
C. Set D.
Range
yR
y ≥ -8
y ≥ -6
y ≥ -6
D. Set C.
or p = 3 B. p = –
or p = –3
D. p = 4 or p = 3
12. Solve 2x2 = 7x – 6 by factoring.
A. x = 2 or x = 3
B. x = –2 or x = –
C. x = 2 or x =
D. x = 6 or x = –1
13. Solve 10x2 + 30x = –2x2 – 30x – 75 by factoring.
A. x = –
or x = 2
B. x = –
C. x = –
or x =
D. x = –
17. Solve 4x2 + 4x – 5 = 0 using the Quadratic Formula.
A. x =
or x =
B. x =
14. Which quadratic function represents this parabola?
or x =
C. x =
or x =
y
5
D. x =
4
or x =
3
18. Solve 2y2 – 3y + 1 = 0 using the Quadratic Formula.
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
A. y = 1 or y = –
B. y = 1 or y = –
C. y = –1 or y =
D. y = 1 or y =
–4
–5
19. Solve 9w2 + 6w + 1 = 0 using the Quadratic
Formula.
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
15. Which quadratic function represents this parabola?
A. w =
B. w = –
C. w = 0 or w = –
D. w = 0 or w =
y
5
20. Solve x2 – 2x = 4 using the Quadratic Formula.
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
A. x = 1 +
B. x = –1 +
C. x = –1 +
D. x = 1 +
or x = 1 –
or x = –1 –
or x = –1 –
or x = 1 –
–2
–3
–4
21. Solve 4b2 – 2b = –3b2 + 2 using the Quadratic
Formula.
–5
A. f(x) = –0.5(x + 1)2 + 6 B. f(x) = 0.5(x + 1)2 + 6
C. f(x) = 0.5(x – 1)2 – 6 D. f(x) = –0.5(x – 1)2 + 6
A. b = –
B. b = –
or b = –
or b = –
2
16. Solve x + 6x + 5 = 0 using the Quadratic Formula.
A. x = 5 or x = 1
B. x = –5 or x = –1
C. x = 5 or x = –1 D. x = –5 or x = 1
Of course, if any equation can be factored, feel free to solve that way.
C. b =
D. b =
or b =
or b =
Short Answer
30. Determine the roots of the corresponding quadratic
equation for the graph.
22. If a parabola with equation y = ax2 + bx + c opens
downward, will a be positive or negative?
23. If a parabola with equation y = ax2 + bx + c has a yintercept above the x-axis, will c be positive or
negative?
24. Make a table of values, then sketch the graph of the
relation y = x2 + 2x + 11.
25. Fill in the table for the graph in #24.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
31. Determine the roots of the corresponding quadratic
equation for the graph.
26. Make a table of values, then sketch the graph of the
relation y = x2 – x + 7.
27. Fill in the table for the relation in #26.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
28. Make a table of values, then sketch the graph of the
relation y = –x2 – 4x + 12.
29. Fill in the table for the relation in #28.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
32. The graph of a quadratic function has x-intercepts 4
and 3. Write a quadratic equation that has these
roots.
33. The graph of a quadratic function has x-intercepts –
2 and –7. Write a quadratic equation that has these
roots.
34. Sketch the graph of f(x) = –(x – 4)2 + 2, then state
the domain and range of the function. [Note that
this is in ‘vertex form.’]
35. Use a graph to determine the equation of a parabola
with vertex (1, 7) and point (4, –20).
Remember to include “let” and “therefore”
statements for word problems like these … →
36. The sum of two numbers is 37. Their product is
312. What are the numbers?
37. Two consecutive integers are squared. The sum of
these squares is 1513. What are the integers?
38. Determine three consecutive positive odd integers,
if the square of the largest integer is 9 less than the
sum of the squares of the two smaller integers.
Problem
39. The height of a golf ball above the ground, y, in
metres, is modeled by y = –4.9x2 + 10x, where x is
the time in seconds after the ball is hit.
a) Determine the maximum height the ball will
reach, rounded to the nearest tenth of a metre.
b) State any restrictions on the domain and range.
c) For how long is the ball in the air?
40. The height, in metres, of a fireworks rocket is
modeled by the function h(t) = –4.9t2 + 20t + 4,
where t = time in seconds after the rocket is fired.
a) Determine the domain and range of the function
to the nearest tenth.
b) Use a table of values to graph the function.
41. The width of a rectangular garden is 2 m less than
its length. Determine the dimensions of the garden if
the area is 36 m2.
42. Identify and correct any errors in this solution.
44. a) Write a quadratic function with zeros at 0.50 and
0.75.
b) Determine two other possible functions with the
same zeros.
45. Tori sells posters to stores. The profit function for
her business is P(n) = –0.3n2 + 4n – 5, where n is
the number of posters sold per month, in hundreds,
and P(n) is the profit, in thousands of dollars.
a) How many posters must Tori sell per month to
break even?
b) If Tori wants to earn a profit of $6000 (P(n)= 6),
how many posters must she sell?
46. A theatre sells tickets to a musical. The profit
function for the show is P(t) = –30t2 + 550t – 400,
where P(t) is the profit and c is the price of each
ticket, both in dollars.
a) What ticket price will result in the theatre
breaking even on the show?
b) What ticket price will raise the most money for
the theatre?
47. a) Suppose someone threw a stone off a 100 m cliff.
The height of the stone, h(t), in metres, after t
seconds is given by h(t) = –4.9t2 + 3.0t + 100. How
long would it take the stone to hit the ground?
b) The height of a stone, h(t), in metres, falling
from a 200 m cliff over time, t, in seconds, can be
modeled by the function h(t) = –4.9t2 + 3.0t + 250.
How long it would take the stone to hit the ground?
48. Gravity affects the speed at which objects travel
when they fall. Suppose a rock is dropped off a 7.5
m cliff on Mars. The height of the rock, h(t), in
metres, over time, t, in seconds could be modeled
by the function h(t) = –1.9t2 + 3.0t + 7.5.
43. Identify and correct any errors in this solution.
a) How long would it take the rock to hit the bottom
of the cliff?
b) The same rock dropped off a cliff of the same
height on Earth could be modeled by the function
h(t) = –4.9t2 + 3.0t + 7.5. Compare the time that the
rock would be falling on Earth and on Mars.
or
or
y
Mathematics 521A: EXAM REVIEW [Ch. 7]
Answer Section
20
18
16
14
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
12
10
C
B
A
D
D
A
C
C
D
D
B
C
B
D
B
B
D
D
B
D
C
8
6
4
2
–5
–4
–3
–2
1
2
3
5
x
5
x
4
25.
(0, 11)
none
x = –1
(–1, 10)
xR
y  10
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
26.
x
–2
–1
0
1
2
3
y
13
9
7
7
9
13
SHORT ANSWER
22. negative
23. positive
24.
x
–3
–2
–1
0
1
–1
y
16
14
12
10
8
y
14
11
10
11
14
6
4
2
–5
–4
–3
–2
–1
–2
1
2
3
4
–4
–6
27.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
(0, 7)
none
x = 0.5
(0.5, 6.75)
xR
y  6.75
Domain
Range
y
4
28.
3
x
–6
–4
–2
0
2
y
0
12
16
12
0
2
1
–3
–2
–1
–1
1
2
3
4
–2
–3
–4
y
16
–5
34.
14
12
35.
36.
37.
38.
10
8
6
y  4, x  R
f(x) = –3(x – 1)2 + 7
13 and 24
27 and 28
7, 9, 11
4
2
PROBLEM
–7
–6
–5
–4
–3
–2
–1
–2
1
2
3
x
39. a)
–4
–6
29.
30.
31.
32.
33.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
There are no roots.
x = 1, x = –3
Answers may vary.
x2 – 7x + 12 = 0
Answers may vary.
x2 + 9x + 14 = 0
(0, 12)
(–6, 0), (2, 0)
x = –2
(–2, 16)
xR
y  16
b) 0  x  2, 0  y  5.1
c) 2.0 s
40. a) 0  x  4.27, 0  y  24.4
b)
5
6
7
x
or
43. The first error is in line 2. When 9y is factored out
of the expression, the remaining factor is
y – 9.
or
44. a)
41. Let l represent the length of the garden, in metres.
Let w represent the length of the garden, in metres.
w=l–2
Let A represent the area of the garden, in square
metres.
lw = A
l(l – 2) = 36
l2 – 2l – 36 = 0
Graph the corresponding function for the equation.
b) Other possible functions are multiples of the
function where a  1.
Examples may vary:
f(x) = 2x2 – 2.50x + 0.650
f(x) = –2x2 + 2.50x – 0.650
45. a)
Tori must sell 140 or 1200 posters before she breaks
even.
The length is 7.083 m.
b)
Therefore, the width is 5.083 m.
42. The first error is in line 1. The number 16 should
have been factored out of the equation.
The second error is in line 5. The square root of a
perfect square can be both negative and positive
values.
Tori must sell 390 or 950 posters to earn a profit of
$6000.
46. a) 0 = –30t2 + 550t – 400
Divide both sides by 10.
a = –3, b = 55, c = –40
or
or
The price of a ticket must be $0.76 or $17.57 for the
charity to break even.
b) The ticket price must be $9.17 for the profit to
reach a maximum of $2120.83.
47.
a) 0 = –4.9t2 + 3t + 200
a = –4.9, b = 3, c = 100
b) 0 = –4.9t2 + 3t + 250
a = –4.9, b = 3, c = 250
or
or
Since time cannot be
negative, the time it
takes for the rock to hit
the water is 4.8 s.
Since time cannot be
negative, the time it
takes for the rock to hit
the water is 7.5 s.
48.
a) 0 = –1.9t2 + 3t + 7.5
b) 0 = –4.9t2 + 3.0t + 7.5
a = –1.9, b = 3.0, c = 7.5 a = –4.9, b = 3.0, c = 7.5
or
Time cannot be a
Time cannot be a
negative value, so the
negative value, so the
time it takes for the rock time it takes for the rock
to hit the bottom of the
to hit the bottom of the
cliff on Mars is 2.9 s.
cliff on Earth is 1.6 s.
Difference in times = 2.927... s – 1.580... s
Difference in times = 1.3 s
The difference in times between the two planets is
1.3 s.