Algebra 2
Final Exam Review (T3): Units 1-5
Name:____________________________________Bk:_____
State the Domain and Range of each graph shown below, then determine if it is a function.
1.
D: ____________________
2.
D: ____________________
R: ____________________
R: ____________________
Function? ______________
Function? ______________
Use these functions to find the following values. 𝒇(𝒙) = 𝟐𝒙𝟐 + 𝟒𝒙 − 𝟓
3.
Solve g(x) = 11
4.
Find g(-1)
and
5.
𝒈(𝒙) = √𝒙 + 𝟓 − 𝟐.
Find f(-4)
Plot and label max/min, degree of the polynomial, x-intercept(s), and y-intercept. Also, write
the behavior “as x approaches negative infinity” and “as x approaches positive infinity”.
6.
Degree of: _________
𝑓(𝑥) → _______
𝑎𝑠 𝑥 → −∞
𝑓(𝑥) → _______
𝑎𝑠 𝑥 → +∞
Graph the following.
7.
y = |𝑥 − 3| + 5
8.
y = (x + 2)3 + 1
9.
y = √𝑥 + 5 − 2
10.
y = -2(x - 1)2 + 4
11.
𝑓(𝑥) = {
2
𝑥
3
− 1 𝑖𝑓 𝑥 ≤ 0
2𝑥 − 8 𝑖𝑓 𝑥 > 2
12.
𝑥3
ℎ(𝑥) = { −2𝑥 + 3
|𝑥| − 2
13. Write the equation for circle shown.
Matching:
14. _____ y  ax 2  bx  c
A. Factored Form
15. _____ y  a( x  b)( x  c)
B. Vertex (graphing) Form
16. _____ y  a( x  h) 2  k
C. Standard Form
𝑖𝑓 𝑥 ≤ 1
𝑖𝑓1 < 𝑥 ≤ 4
𝑖𝑓 𝑥 > 4
17. What does it mean to solve a quadratic function?
18. Solve the following quadratic equation by factoring.
y  2 x 2  5x  3
19. Solve the following quadratic equation by completing the square.
y  x 2  2x  6
20. Solve the following quadratic equation using the quadratic formula.
y  5 x 2  8 x  1
Find the roots of each quadratic function.
21.
y  x 2  6 x  16
22.
y  x2  2x  5
23.
y  3x 2  12 x  5
24.
1
y  ( x  2) 2  7
3
Write a quadratic equation in standard form given each set of roots.
25.
1
, -1
5
26.
 2  5i
27. Find the vertex of the following parabola by averaging the x-intercepts. Then write the
equation in vertex form.
y  x 2  2 x  15
Vertex:
Equation in vertex form:
28. Find the vertex of the following parabola by completing the square. Then write the equation in
vertex form.
𝑦 = −3𝑥 2 + 6𝑥 + 7
Vertex:
Equation in vertex form:
29. Write a quadratic equation in vertex form that represents the following situation.
The dog park by Tammy’s house has a 4 foot fence surrounding a separate play area for small dogs.
While playing at the dog park, Tammy accidentally threw her dog’s ball into the small dog area. Her
dog (which is pretty big) jumped over the 4 foot fence to retrieve his ball. The dog’s take off point was
6 feet away from his landing point. Assume that the path the dog traveled was a parabola.
30. Given the equation and graph of the parabola, find the following information.
𝑦 = 𝑥 2 − 2𝑥 − 8
Equation in vertex form:
Vertex:
x-intercept(s):
y-intercept:
Domain:
Range:
Without a calculator, sketch the graph of each polynomial function. State (as ordered pairs)
and label (on the graph) the zeros of the function.
31.
P( x)  ( x  12)( x  1)( x  5)
32.
F ( x)  3x( x  4)( x  1) 2 ( x  5)
33. Sketch the graph of the following polynomial function if you know one of the roots of the
function is -7. (Hint: use division to find the other roots of the function)
W ( x)  x3  x 2  34 x  56
Simplify. Make sure to write in complex number form.
34.
 121
35.
(6i) 2 (2)
36.
 81x 2
37.
(4  2i)  (3  2i )
38.
(3  2i )(3  2i )
39.
(7  i)  (6  5i )
40.
3i
 5i
41.
(7  i )(3  2i )
42.
3i
2  5i
Sketch a graph given the following information regarding the roots of the function.
43.
6 real roots
44.
2 real roots, 2 complex roots
Simplify using the method of your choice.
45.
(4 x 2  2 x  6)  (2 x  3)
46.
x5  7 x3  x  1
x3
State any restrictions (excluded values) for each.
47.
x4
x3
48.
2w
4w  1
49.
5
k  5k  4
2
Simplify.
50.
5 x 2  10 x  75 2 x 2  10 x  28

4 x 2  24 x  28 x 2  7 x  10
51.
x2 1
x2  4

2 x 2  x  1 2 x 2  3x  2
Simply.
52.
y2  4 y  4
3y2  5y  2
53.
16
2

x  16 x  4
2
54.
5
20
 2
2 w  12 w  4 w  12
Solve.
55.
x
5x  8
x
x2
x2
56.
x 1
12
 4 2
x3
x  2x  3