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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

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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

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f)

g)

h)

3

𝑥−3

4𝑥

𝑥+1

≤

2

𝑥+5

≥3

(𝑥−3)(𝑥+8)

𝑥(𝑥−9)

≥0

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