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CAT Review 3, pt 1
I. Find each of the following for each quadratic function below:
f(x)= -2(x - 3)2 + 8
a) direction it opens?_____
b) Vertex
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c) x-intercepts
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d) y-intercepts
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e) Line of Symm. _____
f) Max/Min? Value _____
g) Domain
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h) Range
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i) graph
g(x)= (x+4)2 +1
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h(x)= -x2 - 2x + 1
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j) Among all pairs of numbers whose sum is -18, find a pair whose product is as
large as possible. What is the maximum product?
k) The base of a triangle measures 40 inches minus twice the measure of its
height. For what measure of the height does the triangle have a maximum area?
What is the maximum area?
l) A company manufactures and sells bath cabinets. The function models the
company’s daily profit, P(x), when x cabinets are manufactured and sold per day.
P(x) = -x2 +150x – 4425.
How many cabinets should be manufactured and sold per day to maximize the
company’s profit? What is the maximum daily profit?
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CAT Review 3, pt 1
II. Use the polynomial functions below for the following questions.
f(x)= x3+3x2–x–3 g(x)= -x4+4x3–4x2 h(x)= (x+1)(2x-3)2 j(x)= x4-2x2+1
a) max # of zeros? turns?
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b) end behavior?
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c) zeros
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d) What happens at each zero?
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e) y-intercept
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f) graph? extras?
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g) Does f(x)= x3 – 2x – 5 have a real zero between two and 3? Explain.
III. Divide – any method.
a) (x2+10x+21)  (x+3)
b) (4 – 5x – x2 + 6x3)  (3x – 2)
c) (6x4 +5x3 + 3x – 5)  (3x2 – 2x)
d) (5x3 +6x + 8)  (x + 2)
e) If f(x)= x3 – 4x2 + 5x + 3, find f(2).
f) Solve 2x3 – 3x2 – 11x + 6 = 0, if 3 is a zero of f(x) = 2x3 – 3x2 – 11x + 6.
874001846, Page 2 of 3
CAT Review 3, pt 1
IV. For each polynomial function or equation, find what is indicated.
f(x)= -x4 + 3x2 + 4
a)Possible zeros
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g(x)= 15x3 + 14x2 – 3x – 2
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f(x)= x3 + 2x2 – 5x – 6
b)Find all zeros
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g(x)= x3 + 7x2 + 11x – 3
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c)Solve
x4 – 6x2 – 8x + 24 = 0
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f(x)= x3 + 2x2 + 5x + 4
d) Positive/Negative zeros (Descartes)
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2x4 + x3 – 17x2 – 4x + 6 = 0
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g(x)= -x4 + 3x2 + 4
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e) Write a polynomial of degree 3, with zeros at 1 and i, where f(-1) = 8.
f) Write a polynomial of degree 4, with zeros at 2(mult. 2) and 3i, where f(0) = 36.
Extra Notes
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