Answers INMT3 Integrated Math 3 Sem 1 26-27Graphs of Polynomial Functions

Graphs of Polynomial Functions — Unit test Answers

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What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

–2, –1, 0, 2

–2, 0, 1, 2

–1, 0

0, 1

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A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeters, 2x centimeters, and x + 6 centimeters. The equation can be used to find x. What is the length of the longest side? Use a graphing calculator and a system of equations to find the answer.

4 centimeters

5 centimeters

8 centimeters

10 centimeters

A function is a sixth-degree polynomial function. How many turning points can the graph of the function have?

exactly 5

5 or less

exactly 6

6 or less

The polynomial function f(x) = 3x5 – 2x2 + 7x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground level? Begin by factoring x to create a constant term.

0, , 1, , 3

0, , 1, , 7

, 1, , 3

, 1, , 7

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

–24, –3, 12

–12, 3, 24

–4, –2, 3

–3, 2, 4

Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

f(x) = x(x – a)2(x – b)4

f(x) = x(x – a)3(x – b)2

f(x) = x4(x – a)(x – b)2

f(x) = x2(x – a)5(x – b)

According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 – 33x2 – 12x + 20., –2, 1, Which is an actual root of f(x)?

Negative five-halves

–2

Ten-thirds

Which system of equations can be graphed to find the solution(s) to 4x2 = x2 + 7?

Option

A polynomial function has a root of –6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

Option

Brian is solving an equation where both sides are quadratic expressions. He sets the expressions equal to y. Then he graphs the system finding that the two graphs share a common vertex, but one graph opens upward and the other opens downward. How should Brian interpret this outcome?

There is exactly one intersection point.

There are exactly two intersection points.

There are exactly three intersection points.

There are infinitely many intersection points.

Which expression is a possible leading term for the polynomial function graphed below?

–18x14

–10x7

17x12

22x9

What is the ninth term in the binomial expansion of (x – 2y)13?

329,472x5y8

–329,472x5y8

–41,184x8y5

41,184x8y5

The president of a company creates a graph of the price of the company’s stock over one year. He describes the graph as follows:• The price of the stock rose to about $17 before falling to about $3.• There have only been two periods during which the price of the stock decreased.• The price of the stock is expected to increase in the long run.Which graph correctly shows the price of the stock?

Option

If 5 + 6i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

–5 – 6i

5 – 6i

6 – 5i

6 + 5i

Which statement about the polynomial function g(x) is true?

If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.

If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.

If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.

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Graphs of Polynomial Functions — Unit test Answers

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