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Algebra II - Chapter 5 Test
PRACTICE************* Mr. Sokoloski
Multiple Choice
Identify the letter of 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
b
____
c
linear function
linear term:
constant term: 18
quadratic function
quadratic term:
linear term:
constant term: 18
d
2. Which is the graph of
?
a
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
2
4
6
8
x
2
4
6
8
x
y
8
–8 –6 –4 –2 O
–2
____
linear function
linear term:
constant term: 18
quadratic function
quadratic term:
linear term:
constant term: 18
–8 –6 –4 –2 O
–2
x
–4
–4
–6
–6
–8
–8
3. Find the missing value to complete the square.
a
9
b
36
c
6
d
81
Short Answer
Identify the vertex and the axis of symmetry of the parabola. Identify ‘mirror’ points
CORRESPONDING to P and Q.(not the points P and Q themselves).
y
4.
8
–8
P
4
–4
O
Q
4
8
x
–4
–8
Vertex ______________
Axis of symmetry _________
Mirror of P __________
Mirror of Q __________
5. Graph
mirror.
. List your vertex, is it a maximum or minimum,axis of symmetry, a point and its
y
8
6
4
2
–8
–6
–4
–2
O
2
4
–2
–4
–6
–8
Vertex ______________
Max or Min ? ___________
Axis of symmetry _________
Point __________
Mirror __________
6
8
x
6.Graph
. Write the vertex form of the function. List your vertex, is it a maximum or minimum,axis of
symmetry, a point and its mirror.
y
8
6
4
2
–8 –6 –4 –2 O
–2
2
4
6
8
x
–4
–6
–8
Vertex form _______________________
Vertex ______________
Max or Min ? ___________
Axis of symmetry _________
Point __________
Mirror __________
7. Use vertex form to write the equation of the parabola.
y
8
6
4
2
–8 –6 –4 –2 O
–2
2
4
6
8
x
–4
–6
–8
8. The function
models the profit a band makes from playing concerts. Here P is the
profit in dollars, and t is the price of a ticket. Write the function in vertex form. Use the vertex form to find
the price that yields the maximum profit and the amount of the profit.
9. Identify the vertex and the y-intercept of the graph of the function
vertex __________
y-intercept ________
10. Factor the expression:
.
11. Factor the expression:
12. Simplify
using the imaginary number i.
13. Simplify –6 –
14. Simplify
15. Simplify
16. Find
.
Solve the equations(you must solve by factoring for one question and solve by completing the square for
one question; solve the others any way you choose).SHOW YOUR WORK TO GET FULL CREDIT.
Write the method you used to solve each question.
17.
“I solved using ___________________________”
18.
“I solved using ___________________________”
19.
“I solved using ___________________________”
20.
21.
22.
“I solved using ___________________________”
“I solved using ___________________________”
“I solved using ___________________________”
23. A bungee tower is 540 feet tall. The function
models the height y in feet of a jumper t
seconds after he/she jumps from the top of the tower.
a. After how many seconds will the person hit the ground(if their bungee is too long)?
Round your answer to the nearest tenth of a second.
b. What is the height of the person 3 seconds after he/she jumps from the top of the tower?
24. Determine the type and number of solutions of
25. Rewrite the equation in vertex form using complete the square.
.
Algebra II - Chapter 5 Test
Answer Section
PRACTICE************* Mr. Sokoloski
MULTIPLE CHOICE
1. ANS: B
DIF: L1
REF: 5-1 Modeling Data With Quadratic Functions
OBJ: 5-1.1 Quadratic Functions and Their Graphs TOP:
5-1 Example 1
2. ANS: B
DIF: L1
REF: 5-3 Translating Parabolas
OBJ: 5-3.1 Using Vertex Form
TOP: 5-3 Example 1
3. ANS: A
DIF: L1
REF: 5-7 Completing the Square
OBJ: 5-7.1 Solving Equations by Completing the Square
TOP: 5-7 Example 2
SHORT ANSWER
4. ANS:
(–2, 4), x = –2;
P'(–1, 3), Q'(–4, 0)
DIF: L1
REF: 5-1 Modeling Data With Quadratic Functions
OBJ: 5-1.1 Quadratic Functions and Their Graphs TOP:
5-1 Example 2
5. ANS:
y
8
6
4
2
–8
–6
–4
–2
O
2
4
6
8
x
–2
–4
–6
–8
DIF: L1
REF: 5-3 Translating Parabolas
TOP: 5-3 Example 1
OBJ: 5-3.1 Using Vertex Form
3
2
6. ANS: Vertex form: y  4( x  ) 2 ,Vertex: (3/2, 0), Minimum, Axis of symmetry x = 3/2 , point ( 0, 9),
mirror (3, 9)
DIF: L1
REF: 5-2 Properties of Parabolas
OBJ: 5-2.2 Finding Maximum and Minimum Values
7. ANS:
DIF: L1
REF: 5-3 Translating Parabolas
TOP: 5-3 Example 2
8. ANS:
; $20; $6050
DIF: L1
REF: 5-7 Completing the Square
OBJ: 5-7.2 Rewriting a Function by Completing the Square
9. ANS:
vertex: (3, –2);
y-intercept: 7
DIF: L1
REF: 5-3 Translating Parabolas
TOP: 5-2 Example 3
OBJ: 5-3.1 Using Vertex Form
TOP: 5-7 Example 7
OBJ: 5-3.1 Using Vertex Form
TOP: 5-3 Example 3
10. ANS:
DIF: L1
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.1 Finding Common and Binomial Factors
TOP: 5-4 Example 1
11. ANS:
DIF: L1
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.1 Finding Common and Binomial Factors
TOP: 5-4 Example 3
12. ANS:
DIF: L1
REF: 5-6 Complex Numbers
Numbers
TOP: 5-6 Example 1
13. ANS:
OBJ: 5-6.1 Identifying Complex
DIF: L1
REF: 5-6 Complex Numbers
Numbers
TOP: 5-6 Example 2
14. ANS:
OBJ: 5-6.1 Identifying Complex
DIF: L1
REF: 5-6 Complex Numbers
OBJ: 5-6.2 Operations With Complex Numbers
15. ANS:
DIF: L1
REF: 5-6 Complex Numbers
OBJ: 5-6.2 Operations With Complex Numbers
16. ANS:
26
DIF: L1
REF: 5-6 Complex Numbers
Numbers
TOP: 5-6 Example 3
17. ANS:
DIF: L1
REF: 5-7 Completing the Square
OBJ: 5-7.1 Solving Equations by Completing the Square
18. ANS:
1
3,
2
DIF: L1
REF: 5-8 The Quadratic Formula
TOP: 5-8 Example 1
19. ANS:
1, –15
DIF: L1
REF: 5-7 Completing the Square
TOP: 5-6 Example 5
TOP: 5-6 Example 6
OBJ: 5-6.1 Identifying Complex
TOP: 5-7 Example 4
OBJ: 5-8.1 Using the Quadratic Formula
OBJ: 5-7.1 Solving Equations by Completing the Square
20. ANS:
3,-8
DIF: L1
REF: 5-5 Quadratic Equations
OBJ: 5-5.1 Solving by Factoring and Finding Square Roots
21. ANS:
3i, 3i
DIF: L1
REF: 5-6 Complex Numbers
OBJ: 5-6.2 Operations With Complex Numbers
22. ANS:
7
TOP: 5-7 Example 1
TOP: 5-5 Example 1
TOP: 5-6 Example 7
8
DIF: L1
REF: 5-8 The Quadratic Formula
TOP: 5-8 Example 1
23. ANS:
a. 5.8 seconds
b. 396 ft
DIF: L2
REF: 5-5 Quadratic Equations
OBJ: 5-5.1 Solving by Factoring and Finding Square Roots
24. ANS:
two real solutions
DIF: L1
REF: 5-8 The Quadratic Formula
TOP: 5-8 Example 4
25. ANS:
DIF: L1
REF: 5-7 Completing the Square
OBJ: 5-7.2 Rewriting a Function by Completing the Square
OBJ: 5-8.1 Using the Quadratic Formula
TOP: 5-5 Example 3
OBJ: 5-8.2 Using the Discriminant
TOP: 5-7 Example 6