SEMESTER 1 EXAM REVIEW
1. (3𝑥 + 2)(3𝑥 − 2)
2. (𝑥 − 7) − (2𝑥 − 7)
3. (3𝑥 + 6) + (2𝑥 − 1)
4. (𝑥 + 7)(𝑥 − 1)
5. (2𝑥 − 1)(𝑥 + 3)
6. (8𝑥 − 5) − (−6𝑥 + 6)
7. If 𝑓(𝑥) = −𝑥 2 + 2𝑥 − 1, find each of the following:
a. 𝑓(0)
b. 𝑓(−2)
c. 𝑓(−3)
d. 𝑓(1)
8. If 𝑔(𝑥) = (2𝑥 − 7)(𝑥 − 1), find each of the following:
a. 𝑔(3)
b. g(1)
c. g(0)
d. g(-1)
9. Using the given form, write the other two forms of the equation.
Standard Form
Vertex Form
Factored Form
a. _________________
b. _________________
c. 𝑦 = (𝑥 − 1)(𝑥 + 3)
a. _________________
b. (𝑥 + 2)2 − 16
c. _________________
a. _________________
b. _________________
c. 𝑦 = (𝑥 − 3)(𝑥 − 5)
a. 𝑦 = 𝑥 2 − 10𝑥 + 25
b. _________________
c. _________________
d. g(1)
10. Correctly factor the following expressions:
a. x2 - 2x – 63
b. x2 + 6x + 8
c. x2 + 4x – 21
d. 3x2 + 11x + 10
e. 8x2 – 11x + 3
f. 2x2 – 7x – 15
g. 3x2 – 5x – 2
h. 6x2 + x – 15
11. Simplify -4(3x – 2)(x + 4)
12. Simplify (5x + 3)(2x + 4)
13. Simplify 6(2x-1)(x-5)
14. Find the vertex of f(x) = x2 + 6x + 8
15. Which quadratic is narrow and which is wide?
y = 3x2
y = 1/5 x2
16. Which quadratic translates up, which translates down, which moves right, and which
moves left?
f(x) = (x-2)2
f(x) = x2+3
f(x) = x2-5
f(x)=(x+7)2
17. Find the vertex and the y intercept of -3(x+1)2+5
18. Find the vertex and the axis of symmetry of y = 2x2+4x-7
19. Find the y intercept and the axis of symmetry of f(x)=-2x2+9x+3
20. Find the value of c to complete the square: x2-16x+c
21. Find the solution to each quadratic function using whatever method you’d like.
a. x2 + 8x + 8 = 0
b. 2𝑥 2 − 𝑥 − 1 = 0
c. 𝑥 2 − 8𝑥 + 8 = 0
d. (𝑥 + 5)2 = 4
e. 𝑥 2 + 5𝑥 + 4 = 0
22. Simplify the following:
𝑖 10
𝑖 40
𝑖 22
𝑖 17
𝑖 32
𝑖 12
𝑖 29
23. Simplify the following:
a.
√12 + √48
b. √80
c 4√20
d. (√8 ) ( √9 )
𝑖 15
4
f. √81𝑥 8
e. 3 + √8 - √2 + 3√5 – 4 - 3√5
3
i. 184
h. (3√2 + 5) (6√2 – 1)
3
g. √−27
1
j. (𝑦 2 )2
24. Find the inverse of each function:
a. 𝑦 = 5𝑥 + 7
1
b. 𝑦 = 3 𝑥 − 2
c. 𝑦 = (𝑥 + 1)2
2
d. 𝑦 = 3 𝑥 − 1
e. 𝑦 = 2𝑥 2 + 2
25. Solve for x, you may have more than one one solution.
a. 2 = |2𝑥 − 2|
b. |𝑥 + 5| − 2 = 8
d. x2 + 4x – 12 = 0
e. 5x2 – 2x + 4
c. (2𝑥 + 1)2 = 4
26. Make an x/y chart and graph f(x) = |x+2| + 3, then find the inverse and graph it.
Are there any points where 𝑓(𝑥) = 𝑓 −1 (𝑥)? If so, say what the point(s) is. If not, explain how
you know.
Fill in the table below using the graphs above. Use interval notation where necessary.
𝑓 −1 (𝑥)
𝑓(𝑥)
Domain a.
a.
Range b.
b.
Maximum c.
c.
Minimum d.
d.
27. For the equation 𝑓(𝑥) = 𝑥 2 + 2𝑥 + 5 , which of the following statements is false?
a. 𝑓(0) = 5
b. 𝑓(1) = 7
c. 𝑓(2) = 13
d. 𝑓(3) = 20
28. For the equation 𝑓(𝑥) = (𝑥 − 2)2 + 3 , which of the following statements is true?
a. 𝑓 −1 (0) =7
b. 𝑓 −1 (7) = 4
c. 𝑓 −1 (5) = 2
d. 𝑓 −1 (4) = 1
29. What is the domain of f-1(x) if f(x) = 3x2 ?
On this True/False section, if the statement is false, correct it to make it true
30. True or False? If f(x) = x, then f-1(x) = x
31. True or False? f(x) = x2 – 7 is a function with 1 real irrational root
32. True or False? f(x) = (x + 2)2 – 5 is a function with a maximum of 5 at x=2
33. True or False? the recursive function f(0) = 1, f(x) = f(x-1) + 2x represents a quadratic function
34. True or False? f(0)=5, f(x)= f(x-1) + 3 is an example of a linear recursive function
35. True or False? the inverse of y = (x-5)2 +2 is a function
36. True or False? x2/3 can be rewritten √𝑥 3
1
1
2
37. True or False? 53 (253 ) = 1253
5
3
38. True or False? if f(x) = 𝑥 3 , then f(4) = 8√4
39. True or False? (√50 + 2) (5 - √8 ) = 21√2 – 10
1
40. True or False? compared to the parent graph, the graph of y = 4 |x| + 3 would be fat & up 3
41. True or False? -2(x+2)2 +4 opens up and has a vertex if (2,4)
42. True or False? 5√7 + √7 = 6√7
43. True or False? 5√7 ( -2√5 ) = 3√35
44. True or False? the domain of the original function is the range of its inverse
45. True or False? f(0) = 4, f(x) = 2(f(x-1) is an example of an exponential explicit function
46. True or False? roots, zeros, answers, and x intercepts are all ways to describe the solutions of an
absolute value function
47. True or False? the denominator of a rational exponent is the index of the radical, while the
numerator is the power
1
48. True or False? 3x-2 = 3𝑥 2
1
1
49. True or False? 255 = (52 )5
50. Is the function, f ( x)  3( x  2)( x  1) , linear, quadratic, or exponential? Justify your answer.
51. Is the function to the left linear, quadratic, or exponential?
Justify your answer.
x
f(x)
-2
1
4
1
2
-1
0
1
1
2
2
4
52. A zombie population starts with 30 zombies and the zombie hoard can eat 15 other zombie
brains per hour. But notice, the zombie hoard is still being hunted by humans! We can use
the function 𝑓(𝒙) = −𝟐𝒙𝟐 + 𝟏𝟓𝒙 + 𝟑𝟎 to calculate how many zombies there will be at any
given hour (x).
A. What does 𝑓(2) mean in this context?
B. Draw a graph to model this context. Label
your axes and show your scale.
Use your graph and/or table to answer the
following.
C. Explain the meaning of 𝑓(𝑥) = 0 in this
context? Estimate the value of x that
makes this statement true.
D. What is the largest population of zombies?
When will that happen?