ALG. 2 CH. 5.1-5.4 TEST REVIEW - QUADRATIC EQUATIONS & FUNCTIONS
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant
terms.
____
____
1.
a. linear function
linear term:
constant term: 6
b. quadratic function
quadratic term:
linear term:
constant term: 6
c. linear function
linear term:
constant term: –6
d. quadratic function
quadratic term:
linear term:
constant term: –6
a. linear function
linear term:
constant term: –6
c. quadratic function
quadratic term:
linear term:
constant term: –6
d. linear function
linear term:
constant term: –6
2.
b. quadratic function
quadratic term:
linear term:
constant term: –6
Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q.
____
y
3.
8
4
Q
–8
–4
O
P
4
8
x
–4
–8
a. (–1, –2), x = –1
P'(0, –1), Q'(–3, 2)
b. (–2, –1), x = –2
P'(–2, –1), Q'(–1, 2)
c. (–1, –2), x = –1
P'(–2, –1), Q'(–1, 2)
d. (–2, –1), x = –2
P'(0, –1), Q'(–3, 2)
____
y
4.
8
4
P
–8
–4
O
4
8
x
Q
–4
–8
____
a. (–3, 1), x = –3;
c. (–3, 1), x = –3;
P'(–2, 0), Q'(–5, –3)
P'(–4, 0), Q'(–1, –3)
b. (1, –3), x = 1;
d. (1, –3), x = 1;
P'(–2, 0), Q'(–5, –3)
P'(–4, 0), Q'(–1, –3)
5. Find a quadratic function to model the values in the table. Predict the value of y for x = 6.
x
y
–1
2
0
–2
3
10
a.
b.
c.
d.
; –58
; 60
; 58
; –58
Find a quadratic model for the set of values.
____
____
6. (–2, 8), (0, –4), (4, 68)
a.
b.
c.
d.
7. A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lake’s
population of waterfowl on each of the next six weeks.
Week
0
1
2
3
4
5
6
Population
585
582
629
726
873
1,070 1,317
a.
Find a quadratic function that models the data as a function of x, the number of weeks.
b.
Use the model to estimate the number of waterfowl at the lake on week 8.
a.
b.
c.
; 1,614 waterfowl
; 2,679 waterfowl
; 1,961 waterfowl
d.
____
____
; 2,201 waterfowl
8. A manufacturer determines that the number of drills it can sell is given by the formula
, where p is the price of the drills in dollars.
a. At what price will the manufacturer sell the maximum number of drills?
b. What is the maximum number of drills that can be sold?
a. $60; 285 drills
c. $31; 2,418 drills
b. $30; 2,415 drills
d. $90; 8,385 drills
9. Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the
formula
, where x is the number of units produced per week, in thousands.
a. How many units should the company produce per week to earn the maximum profit?
b. Find the maximum weekly profit.
a. 1,000 units; $1300
b. 3,000 units; $100
____ 10. Which is the graph of
a.
c. 1,000 units; $600
d. 2,000 units; $1100
?
c.
y
y
8
8
6
6
4
4
2
2
–8 –6 –4 –2 O
–2
2
4
6
8
–8 –6 –4 –2 O
–2
x
–4
–4
–6
–6
–8
–8
b.
d.
y
8
6
6
4
4
2
2
2
4
6
8
x
–8 –6 –4 –2 O
–2
–4
–4
–6
–6
–8
–8
____ 11. Use vertex form to write the equation of the parabola.
4
6
8
x
2
4
6
8
x
y
8
–8 –6 –4 –2 O
–2
2
y
8
6
4
2
–8 –6 –4 –2 O
–2
2
4
6
8
x
–4
–6
–8
a.
b.
c.
d.
____ 12. Identify the vertex and the y-intercept of the graph of the function
a. vertex: (–2, 5);
c. vertex: (2, 5);
y-intercept: –7
y-intercept: –7
b. vertex: (2, –5);
d. vertex: (–2, –5);
y-intercept: –12
y-intercept: 9
____ 13. Write
a.
b.
in vertex form.
c.
d.
Write the equation of the parabola in vertex form.
____ 14. vertex (0, 3), point (–4, –45)
a.
b.
c.
d.
Factor the expression.
____ 15.
a.
b.
c.
d.
a.
b.
c.
d.
____ 16.
Short Answer
Factor the expression.
17.
.
18.
19.
20.
21.
22.
23.
Write the equation of the parabola in vertex form.
24. vertex (–4, 3), point (4, 131)
Find a quadratic model for the set of values.
25.
x
–2
0
4
f(x)
1
–3
85
ALG2 CH. 5.1-5.4 TEST REVIEW
Answer Section
MULTIPLE CHOICE
1. ANS: C
2. ANS: B
3. ANS: A
4. ANS: A
5. ANS: C
6. ANS: A
7. ANS: C
8. ANS: B
9. ANS: A
10. ANS: A
11. ANS: C
12. ANS: A
13. ANS: D
14. ANS: B
15. ANS: C
16. ANS: B
SHORT ANSWER
17. ANS:
18. ANS:
19. ANS:
20. ANS:
21. ANS:
22. ANS:
23. ANS:
24. ANS:
25. ANS: