Math 3 Unit 3 Review Packet Read and follow all directions
carefully. Show your work.
Place answers in answer column
when is provided.
1.
Let y = −
1
( x + 1)( x − 5)
2
a. y-intercept.
b. x-intercepts
c. vertex
d. axis of symmetry.
2.
Let y = (x + 3)2 − 4
a. y-intercept.
b. x-intercepts
c. vertex
d. axis of symmetry.
Name: For questions 3 - 7, simplify each indicated operation with complex numbers.
3.
(−3 + 4i) + (−6 − 2i )
3.
_______________
4.
(−3 + 4i) − (−6 − 2i )
4.
_______________
5.
(−3 + 4i)(−6 − 2i)
5.
_______________
6.
(7 − 3i ) − (4 + 9i ) + (1 − 2i )2
6.
_______________
For questions 7 – 11, solve the following quadratic equations by the method requested.
7. [Square Root Method]
a)
1− x 2 = 50
b) −3( x − 2 ) = −15
2
8.
a)
[Complete the Square]
9.
a)
[Factoring]
x 2 − 5 x − 14 = 0
10.
[Quadratic Formula]
For the quadratic equation 2 x 2 − 4 x + 5 = 0 ,...
x 2 + 5x + 8 = 0
b) x 2 + 16 x + 10 = 0
b) 6x − 13x − 28 = 0
2
a. State the discriminant. Describe what types of zeros you’ll get.
b. Solve by using the quadratic formula.
11.
Solve the following by the method of your choice:
x 2 − 12 x + 100 = 0
12.
Solve by any method you choose:
x2 + 4x + 29 = 0
13.
Solve by any method you choose:
-3x2 = 7x
14.
Solve by any method you choose:
(x − 1)2 − 20 = 0
15.
Write the following in Standard Form:
16.
1
Write the following in Vertex Form: y = − x 2 + 6 x − 5
2
y = 3( x + 1) 2 + 4
For questions 22 - 29, choose the best answer and place the corresponding letter in the blank.
_____
17.
What is the vertex of the graph of y = 2(x − 3) + 4 ?
A. (−3, 4)
B. (3, 4 )
C. (3, − 4)
D. (−3, − 4)
_____
18.
If b − 4ac < 0 , then the type and number of zeros for the quadratic equation are
which of the following?
A. One real and one imaginary
B. One real
C. Two imaginary
D. Two real
2
2
_____19.If ax + bx + c is a perfect square trinomial, then the graph of y = ax + bx + c has
exactly how many x-intercepts?
A. Three
B. Two
C. One
D. None
2
______20.
2
Simplify completely:
a) i
i23
b) -1
c) -i
d) 1
41
_____
21.
Which of the following is equivalent to i ?
A. i
B. −1
C. −i
D. 1
_____
22.
Which of the following quadratic equations is in vertex form?
2
A. y = ( x − 4)( x + 7)
B. y = 2(x − 4) + 3
C. y + 3x = 2x − 3x + 1
2
_____
23.
1
1
x+
4
8
2
1
2
C. x + x +
3
9
2
25.
24.
2
2
x − 1.4
5
Which of the following is a perfect square trinomial?
A. x +
_____
D. y = −5x +
B. 25x + 5x +1
2
D. 9x + 16
2
In which direction does the parabola y = −2x + 5x + 7 open?
A. Up
B. To the right
C. Down
D. To the left
2