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TRASHKETBALL
PRECALCULUS
CHAPTER 2 QUIZ
WHAT IS THE VERTEX
AND WHAT ARE THE INTERCEPTS?
2
1.𝐹 𝑋 = (𝑋 − 4) −4
WHAT IS THE VERTEX
AND WHAT ARE THE INTERCEPTS?
2.F(X) = 3 −
2
𝑋
− 4𝑋
WRITE THE VERTEX FORM OF THE
QUADRATIC EQUATION THAT HAS
THE INDICATED VERTEX AND PASSES
THROUGH THE GIVEN [POINTT?
3. VERTEX: (1, -4)
POINT: (2, -3)
WORD PROBLEM?
4. AN ONLINE MUSIC COMPANY SELLS SONGS FOR $1.75
EACH. THE COMPANY’S COST, C, IS MODELED BY
C =0.0005𝑥 2 + 500 (x is the number of songs sold)
Therefore the company’s profit is given by
P =1.75𝑥 − (0.0005𝑥 2 + 500)
FIND THE MAXIMUM NUMBER OF SONGS PER WEEK
THAT THE COMPANY NEEDS TO SELL TO MAXIMIZE THEIR
PROFIT.
THEN FIND THE COMPANY’S MAXIMUM PROFIT
What transformations are made from
2
the parent function y = 𝑥 to get this
function?
5. F(X) = −(𝑋 − 7)2 + 2
What transformations are made from
5
the parent function y = 𝑥 to get
this function?
6. F(X) = 3 −
1 5
𝑥
2
Use the Leading Coefficient test to
describe the right-hand and left-hand
behavior of the graph
7. F(X) = −𝑥 2 + 6𝑥 + 9
Use the Leading Coefficient test to
describe the right-hand and left-hand
behavior of the graph
8. F(X)
1 3
= 𝑥
2
+ 2𝑥
Find the zeros of this function
algebraically
9. F(X) = 𝑥 4 + 𝑥 3 − 2𝑥 2
Find a polynomial function that has
the given zeros.
#10.
-2, 1, 1, 5
Find a polynomial function that has
the given zeros.
11. 3, 2 − 3, 2 +
3
Divide these polynomials
12.
(5𝑥 3 − 13𝑥 2 − 𝑥 + 2) ÷ (𝑥 2 − 3𝑥 + 1)
Divide these polynomials
3
𝑥 + 2𝑥 − 1
13.
𝑥+3
Use the remainder theorem to evaluate
the function at each of the given values
14.
4
3
2
𝑓 𝑥 = 𝑥 + 10𝑥 − 24𝑥 + 20𝑥 + 44
(a) f(2)
(b) f(-2)
Verify that the given factors are
factors of the function:
3
2
15. 𝑓 𝑥 = 𝑥 + 4𝑥 − 5𝑥 −28
Factor: (x-4)
Use the Rational Zero Test to list all
possible rational zeros of f(x):
3
2
16. 𝑓 𝑥 = 4𝑥 − 11𝑥 + 10𝑥 −3
Use Descarte’s Rule of Signs to
determine the possible numbers of
positive and negative real zeros of
the function:
3
2
17. 𝑓 𝑥 = 6𝑥 − 5𝑥 + 24𝑥 − 20
Perform the operation and write the
result in standard form:
18.
a. (7 + 5i)+(-4+2i)
b. 5i(13-8i)
c. (1 + 6i)(5 – 2i)
Perform the operation and write the
result in standard form:
19.
3 + 2𝑖
5+𝑖
Find all the real zeros of the function
and write the polynomials as a
product of linear factors.
4
3
20. 𝑓 𝑥 = 2𝑥 − 5𝑥 + 10𝑥 − 12