### Algebra 2 Fall Semester Review

```Name____________________________________
Algebra 2 Fall Semester Review
Directions: Answer each question as completely as possible. If you do not have enough space, you may use a
separate sheet of paper and attach it.
1) Determine if each relation is function.
____________
____________
___________
____________
2) For π(π₯) = 2π₯ β 9 and π(π₯) = 10π₯, find
π(β3) =__________________
π(π(4)) = __________________
Find the inverse of each function.
3) π(π₯) = βπ₯ + 2
5) Solve the following system of equations: {
1
π (2) = __________________
π(π(β1)) = __________________
4) π(π₯) = π₯ 2 + 6
4π₯ + 2π¦ = 20
β2π₯ β 2π¦ = 10
βπ₯ β 5π¦ + π§ = 17
6) Solve the following system of equations using matrices. { β5π₯ β 5π¦ + 5π§ = 5
2π₯ + 5π¦ β 3π§ = β10
7) The booster club sold 19 t-shirts, 12 hats, and 8 blankets Monday for \$330. On Tuesday, they sold 7 tshirts, 15 hats, and 12 blankets for \$400. Wednesday they sold 23 hats for \$230. How much is each tshirt, hat, and blanket?
8) Write the system of inequalities for the graph:
9) Graph the system of inequalities on the graph below and list two points in the solution.
1
{π¦ < 3 π₯ + 2
π₯β₯5
Solve the following absolute value equations.
1
10) 3 |5π₯| β 4 = 21
11) |3π₯ β 2| β 6 = β5
Solve the following absolute value inequalities and graph the solution on the number line.
12) |2π₯ β 1| < 7
1
13) |3 π₯| + 5 β₯ 10
State the attributes of the following functions.
14) π(π₯) = 2|π₯ β 3| + 4
15) π(π₯) = β|π₯| β 5
Vertex: ______________
Vertex: ______________
Axis of Symmetry: _______ Max/Min: ___________
Axis of Symmetry: _______ Max/Min: ___________
Domain: _______________ Range: ______________
Domain: _______________ Range: ______________
x-intercept(s): __________ y-intercept: __________
List
the transformations of the following function
x-intercept(s): __________ y-intercept: __________
1
17) π¦ = β 2 |π₯ β 3|
16) π¦ = 2|π₯ + 1| + 1
18)
Graph and state the attributes to the following quadratic functions.
19) π(π₯) = 2(π₯ β 1)2
20) π¦ = π₯ 2 β 2π₯ + 5
Vertex: ________________
Vertex: ________________
Axis of Symmetry: _______
Axis of Symmetry: _______
Max/Min: ______________
Max/Min: ______________
Domain: _______________
Domain: _______________
Range: ________________
Range: ________________
Write the quadratic function, in vertex form, with the given vertex and passes through the given point.
21) vertex at (β2,5) and passes through (β1,4)
22) vertex at (1,2) and passes through (0,5)
Write the quadratic function that passes through the given points.
23)
x
y
-2
39
3
14
5
32
24) {(0, β32), (5, β17), (6, β20)}
25) The given table represents the height of a bottle rocket as it flies up and returns to the ground. Find a
quadratic function to model the data as a function of x, time in the air. Use the model to determine the
height of the rocket at 3 seconds.
Time
Height
Elapsed (s)
0
2
4
Factor the following expressions.
26) 5π2 π + 10ππ2
27) π¦ 2 β 81
(ft)
5
11
13
28) 2π₯ 2 + 20π₯ + 48
29) What are the solutions? 10π₯ 2 + π₯ = 3
30) Solve using the quadratic formula. 5π₯ 2 + 2π₯ = 11
31) The parabola π¦ = 3(π₯ β 5)2 β 6 has vertex (5, β6). If the parabola is shifted 5 units to the right and
up 5 units, what is the equation of the new parabola?
Simplify the expression. Write in π + ππ form.
32) (β9 + 7π) β (11 + 16π)
34) If π΄ = [
β2 5
11
]and π΅ = [
β4 β6
7
β5
], what is π΄ + π΅?
2
33) (5 β 11π) + (7 β 15π)
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