Download Algebra 2: Semester 1 Review Packet

Algebra 2: Semester 1 Review Packet
Section I: Equations
Write the equation of the line…
1. with slope of 5 and y-intercept of -8
2. with slope of -2 and passing through (3, 7)
3. passing through (-2, 5) and (3, 25)
4. passing through (6, 19) and (2, 9)
Write the equation of the line…
5. parallel to y = 4x – 5, and
passing through (5, 1).
6. parallel to y = -8x + 14, and passing
through (10, -49).
7. perpendicular to y = 7x – 5, and
through (21, 10).
8. parallel to y = -8x + 14, and passing
through (12, -13).
Number of
Video Games
Mr. Chute
Owns
2003
21
2005
29
2007
37
2012
57
2020
89
Find the x-intercepts of each function by either factoring or the Quadratic Formula, and
classify the roots by the appropriate number system.
9. Write the equation of the line given the data on the right
(let t = 0 represent the year 2003).
Time (in
years)
10. f(x) = x2 + 8x + 15
11. g(x) = x2 – 8x + 12
12. q(x) = x2 + 7x – 18
13. p(x) = x2 + 14x + 35
14. r(x) = x2 – 3x – 40
15. n(x) = x2 + x – 90
16. v(x) = 3x2 + 9x – 30
17. z(x) = 7x2 – 35x – 28
18. n(x) = -2x2 – 8x + 24
19. f(x) = -3x2 + x + 1
20. g(x) = 2x2 + 11x – 4
21. q(x) = 4x2 – 3x + 2
Solve by substitution.
22. { x + 3y = 19
3x + 4y = 22
23. { 2x – 3y = -2
4x + y = 24
24. { 2x – 3y = 19
4x + y = 17
25. { x + 3y = 16
3x + 4y = 18
Solve by elimination.
26. { 8x + 4y = -48
3x – 4y = -29
27. { 5x + 2y = 20
5x – 3y = -5
28. { 8x + 4y = 32
3x – 4y = 23
29. { 4x + 6y = -2
5x – 3y = 29
30. Mr. Chute is overseeing a pre-school for humans and kittens. It is recess time, and the
students are out on the playground. Mr. Chute counts a total of 27 heads and 90 legs.
How many humans and kittens are there?
Solve for x in each equation.
31. 7x3 + 3(x3 + 5) – 28 = 2x3
32. -4(x4 + 5) + 7(x4 – 1) = 3
33. 6(x5 – 4) + 10x5 – 3(6 – 2) = 1
34. -3(x3 + 7 – 5x3 – 18 + 2x3) = -23
35. x3 + 7x2 + 10x = 0
36. x4 – 3x2 – 4 = 0
37. x3 – x2 – 4x = -4
38. 2x5 – 4x4 – 48x3 = 0
Section II: Graphs
Find the x- and y-intercepts of each line:
1. y = 6x – 18
2. f(x) = -5x + 27
3. 4x + 7y = 56
4. -5x + 6y = 120
Given a starting function of f(x) = x2, describe the transformations in the new function of…
5. g(x) = x2 + 7
6. h(x) = (x – 4)2
7. a(x) = (x – 7)2 – 6
8. b(x) = (x + 6)2 + 1
9. c(x) = -(x – 11)2 + 8
10. d(x) = -3(x + 2)2 – 4
Using a table and the accompanying, plug in numbers to plot each function and identify the
relevant features.
11. f(x) = -2x2 + 4x + 7
12. g(x) = 3x2 + 4x – 2
Axis of Symmetry:
Axis of Symmetry:
Vertex:
Vertex:
13. f(x) = x3 – 3x2 – 4x + 12
14. g(x) = 2x4+ 4x3 – 3x2 – 4x + 1
Local Maxima:
Local Maxima:
Local Minima:
Local Minima:
Increasing Intervals:
Increasing Intervals:
Decreasing Intervals:
Decreasing Intervals:
End Behavior:
End Behavior:
Given a starting function of f(x) = x2, write the new function g(x) with these new
transformations included:
15. shifted left 5 units, down 4 units,
16. shifted right 2 units, up 5 units,
reflected over x-axis
vertically compressed by factor of ¼
g(x) =
g(x) =
17. shifted right 12 units, down 4 units,
reflected over x-axis
18. shifted left 13 units, up 9 units,
vertically stretched by factor of 2/3
g(x) =
g(x) =
Section III: Analysis
Batman throws a Batarang high into the air, such that its motion is modeled by the function
h(t) = -16t2 + 142t + 6.16, where t is time (in seconds), and h(t) represents the height of the
Batarang (in feet).
1. What is the highest height the Batarang will ever reach? At what time does this occur?
2. Using a graphing calculator or the Quadratic Formula, find when the Batarang will hit the
ground.
3. Using a graphing calculator, find (to the nearest hundredth) when the Batarang will be at
a height of 17 feet.
4. Use linear regression to find the equation of the line of best fit to the data below.
Mass (in grams)
Stretch (in cm)
10
20
30
40
50
7.8
11.4
14.8
19.5
23.9
5. Explain correlation in simple terms.
6. How can one determine if there is a strong relationship in the data based on the
correlation coefficient between the two variables?
7. Explain how the terms “turning point”, “increasing”, and “decreasing” are related.
8. Sketch a function f(x) where…
- f has roots are at -2 and 6,
- the y-intercept is 10
- f is increasing for    x  0.5; 3  x  5
- f is decreasing for  0.5  x  3; 5  x  