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Algebra 2 Intensified
Review for Ch. 5 Test
Calculator Allowed
Questions 1 – 7: Use the standard form method to graph the function f ( x)  2  6 x  3x 2 . Show your
work!
1) Find the vertex.
2) Find the y-intercept.
4) Complete the x-y chart and graph.
3) What is the axis of symmetry?
5) State the maximum or minimum.
6) State the domain and range in interval notation.
Domain:
Range:
7) Find the zeros. (round to 3 decimal places)
Directions: For 8 – 11, FACTOR and Solve.
8) 8 x 2  48  40 x
9) 24 x 2  15  2 x
10) Write a quadratic equation with the following roots. Write the equation in the form ax 2  bx  c  0 , where
a, b, and c are integers.
5
1
a.  and 7
b.
3
4
Directions: For 11 – 12, Solve by using the QUADRATIC FORMULA. Leave answer in radical form.
(you must use the quadratic formula for full credit)
11) x 2  7 x  13  0
12) 4 x 2  16 x  3  0
Directions: For 13 – 14, find the discriminant and describe the number and type of roots.
13) 5 x 2  5 x  4  0
14) 42 x  9 x 2  49
Directions for #15 - 20: Factor completely. If not factorable, write prime.
15) 6 y 2  23 y  20
16) 16 x5  79 x 4  5 x3
17) 32r 3  338r
18) 2 x3 y  x 2 y  5xy 2  xy 3
19) 4ab  2a  6b  3
20) x 2  x  1
21) Factor completely and solve.
4 x 4  12 x3  9 x 2  27 x  0
No Calculator
22) Find the value of c that makes the trinomial a perfect square. Then, write the trinomial as a perfect
square.
3
a. x 2  20 x  c
b. x 2  x  c
8
Directions: For 23 – 24, Solve by COMPLETING THE SQUARE. Leave answer in radical form. (you
must use the completing the square method for full credit)
23) 4 x 2  32 x  15  0
24) 8 x 2  13x  4
25) The graph of a quadratic function is shown below. What are the solutions of the related quadratic
equation?
Directions: For 26 – 29, solve using the method of your choice. Find exact solutions!
26) x 2  4 x  29
27) x 2  8 x  16
28) 7 x 2  4 x
29) 4  x  3  1  27
2
Directions: For 30 – 31, write the equation in vertex form. Then, identify the vertex, axis of symmetry,
determine the direction of opening, and say whether it’s wider or narrower than the parent graph y  x 2 .
30) y  2 x 2  16 x  7
31) y  3x 2  9 x  8
Directions: For 32 – 33, write an equation in vertex form for the parabola with the given vertex that
passes through the given point.
32) vertex:
point:
 1, 5
 2,  4
33) vertex:
point:
 5,  3
 1, 5
34) Change the equation to vertex form. Then, analyze the function and then graph it. y  2 x 2  8 x  1
Equation in vertex form:
Analysis: Answer the following.
Vertex:
Axis of Symmetry:
Direction of opening:
Wider or narrower than y  x 2 ?
The graph is translated _____ units __________ and _____ units __________.
Now, graph the function below.
35) Solve.
2 2
x  30  0
3
16) Simplify.
a. 5(6  4i)  (7  11i)  (6  3i)
b.
 3  2i 5  4i 
37) Evaluate i 30
a)  i
38) Simplify
d) -1
1  2i
2  3i
a) 4  7i
39) Evaluate
c) i 2
b) i
b)
4  7i
13
c)
8  7i
7
d)
8i
7
15  24
b) 6 10
a) 6 10
d) 2 15
c) 2 15
40) Factor completely 7 y 2  32 y  15 .
a) (7 y  3)( y  5)
b) (7 y  3)( y  5)
c) (7 y  3)( y  5)
d) (7 y  3)( y  5)
c) 34  30i
d) 16
41) Simplify (5  3i) 2 .
a) 16  30i
b) 34