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MTH 001 – HW3
Chapter 3
Spring 2020
Name:
ID:
Question 1: Write the answers in the form of 𝑎 + 𝑏𝑖.
a) (4 − √−9 )(3 + √−25 )
b)
2+3𝑖
1−2𝑖
Question 2: Simplify:
a) 𝑖 284 − 𝑖1247
b) (−𝑖)89
1
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Question 3: Solve by completing the square.
3𝑥 2 − 12𝑥 + 18 = 0
Question 4: Solve by using the quadratic formula.
a) 2𝑥 2 − 4𝑥 = −3
b) 3𝑥 2 + 2𝑥 = 9
2
Question 5: Let 𝑓(𝑥) = 𝑥 2 − 2𝑥 − 8 .
a) Find the x- intercepts and y- intercepts of 𝑓(𝑥).
b) Find the vertex and axis of symmetry for 𝑓(𝑥).
c) Determine whether there is a maximum or minimum value and find that value.
d) Graph the function of 𝑓(𝑥).
3
Question 6: Let 𝑓(𝑥) = −𝑥 2 − 4𝑥 + 5 .
a) Find the x- intercepts and y- intercepts of 𝑓(𝑥).
b) Find the vertex and axis of symmetry for 𝑓(𝑥).
c) Determine whether there is a maximum or minimum value and find that value.
d) Graph the function of 𝑓(𝑥).
4
Question 7: Solve the following:
3𝑥+7
3𝑥+4
𝑥+1
a)
+
=
𝑥 2 +5𝑥
𝑥+5
𝑥
b)
3𝑥+2
𝑥−2
1
−2
𝑥
𝑥 2 −2𝑥
+ =
c) √2𝑥 − 5 − √𝑥 − 3 = 1
d) ⌈3𝑥 − 1⌉ − 3 = 5
5
Question 8: Solve the following inequalities and represent your solution in interval notation:
a) 7 − |2𝑥 − 5| < 3
b) |2𝑥 + 5| − 4 ≤ 2
c) |𝑥 + 5| + 4 < 1
d) ⌈2𝑥 − 7⌉ ≥ −4
e) 𝑥 3 − 3𝑥 2 − 10𝑥 > 0
6
f)
g)
h)
3
𝑥−3
4𝑥
𝑥+1
≤
2
𝑥+5
≥3
(𝑥−3)(𝑥+8)
𝑥(𝑥−9)
≥0
7
