Name_____________________________________
2nd Six Weeks Test REVIEW
Solve the following absolute value equations.
1
3
1) . |5𝑥| − 4 = 21
2) |3𝑥 − 2| − 6 = −5
Solve the following absolute value inequalities and graph the solution on the number line.
1
3) |2𝑥 − 1| < 7
4) | 𝑥| + 5 ≥ 10
3
State the attributes of the following functions.
5) 𝑓(𝑥) = 2|𝑥 − 3| + 4
6) 𝑓(𝑥) = −|𝑥| − 5
Vertex: ______________
Vertex: ______________
Axis of Symmetry: _______ Max/Min: ___________
Axis of Symmetry: _______ Max/Min: ___________
Domain: _______________ Range: ______________
Domain: _______________ Range: ______________
x-intercept(s): __________ y-intercept: __________
x-intercept(s): __________ y-intercept: __________
List the transformations of the following functions from the parent function.
1
2
7) 𝑦 = 2|𝑥 + 1| + 1
8) 𝑦 = − |𝑥 − 3|
9)
10)
11) 𝑦 = −3𝑥 2 + 4
12) 𝑦 = (𝑥 + 5)2 − 3
Graph and state the attributes to the following quadratic functions.
13) 𝑓(𝑥) = 2(𝑥 − 1)2
14) 𝑓(𝑥) = −3𝑥 2 + 4
Vertex: ________________
Vertex: ________________
Axis of Symmetry: _______
Axis of Symmetry: _______
Max/Min: ______________
Max/Min: ______________
Domain: _______________
Domain: _______________
Range: ________________
Range: ________________
Convert the following quadratic functions to vertex form and state the attributes.
15) 𝑦 = 𝑥 2 − 2𝑥 + 5
16) 𝑦 = 3𝑥 2 + 18𝑥 − 7
Vertex: ________________
Axis of Symmetry: _______
Max/Min: ______________
Domain: _______________
Range: ________________
Vertex: ________________
Axis of Symmetry: _______
Max/Min: ______________
Domain: _______________
Range: ________________
Write the quadratic function, in vertex form, that has the given vertex and passes through the given point.
17) vertex at (−2,5) and passes through (−1,4)
18) vertex at (1,2) and passes through (0,5)
Write the quadratic function that passes through the given points.
19)
20) {(0, −32), (5, −17), (6, −20)}
x
-2
3
5
y
39
14
32
21) 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.
Factor the following expressions.
22) 5𝑚2 𝑛 + 10𝑚𝑛2
23) 𝑦 2 − 81
25) 36𝑥 2 − 4
26) 3𝑏 2 + 14𝑏 − 5
Time
Elapsed (s)
0
2
4
24) 𝑥 2 + 10𝑥 + 24
Height
(ft)
5
11
13