Answers PBCSD_Grade_Forgiveness_1200330_Algebra 2_S1_2024Unit Test

Unit Test — Unit test Answers

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Carlos graphed the system of equations that can be used to solve .What are the roots of the polynomial equation?

–3, –2, 3

–3, 2

18, 32

18, 32, 66

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A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.

4 inches

5 inches

9 inches

10 inches

Which of the following describes the roots of the polynomial function ?

–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3

–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4

2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3

2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

Option

The real root of the equation x3 + 10x2 + 29x + 30 = 0 is –6. What are the nonreal solutions?

2 + i, 2 – i

–2 + i, –2 – i

–4 + 2i, –4 – 2i

4 + 2i, 4 – 2i

What are the possible degrees for the polynomial function?

degrees of 6 or greater

even degrees of 6 or greater

degrees of 5 or greater

odd degrees of 5 or greater

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

f(x) = x2(x – a)2(x – b)4(x – c)

f(x) = x3(x – a)3(x – b)(x – c)2

f(x) = x4(x – a)(x – b)3(x – c)3

f(x) = (x – a)2(x – b)(x – c)6

Which of the following is the complete list of roots for the polynomial function ?

–3 + 2i, –3 – 2i

–2, –4

–2, –4, –3 + 2i, –3 – 2i

–2, –4, –3 + 2i, 3 + 2i

Which graph represents an odd function?

There are 6 points on a coordinate plane. The points are (negative 5, 3), (negative 3, 1), (negative 1, 1), (1, 3), (3, negative 5), (5, negative 1).

There are 8 points on a coordinate plane. The points are (negative 4, 2), (negative 3, negative 1), (negative 1, negative 3), (0, 1), (1, 0), (2, negative 4), (4, 5), (5, 4).

There are 8 points on a coordinate plane. The points are (negative 4, 0), (negative 3, 1), (negative 2, negative 3), (negative 1, negative 2), (1, 2), (2, 3), (3, negative 1), (4, 0)

There are 11 points on a coordinate plane. The points are (negative 4, 3), (negative 4, 4), (negative 3, 5), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 1), (2, 1), (3, 5), (4, 3), (4, 4).

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

–4x8

–4x5

4x5

4x8

The real roots for the equation x4 – x3 + 10x2 – 16x – 96 = 0 are –2 and 3. What are the nonreal solutions?

–i, i

–2i, 2i

–4i, 4i

–16i, 16i

According to the Rational Root Theorem, which is a factor of the polynomial f(x) = 3x3 – 5x2 – 12x + 20?

2x + 1

2x – 1

3x + 5

3x – 5

Which of the following is an odd function?

f(x) = x3 + 5x2 + x

f (x) = StartRoot x EndRoot

f(x) = x2 + x

f(x) = –x

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

, , , 5

, 1, , 11

, , , , , 5, 11

0, , , , , , 5, 11

The owner of a coffee shop chain creates a graph representing sales in thousands of dollars. She describes the characteristics as follows:• There have been two turning points in sales this year.• Sales are expected to increase in the long run.• The least amount of sales during the year is about $250,000.Which graph correctly shows the coffee shop’s sales?

Option

The polynomial function is graphed below.Which is a potential rational root of f(x) at point P?

The root at point P may be .

Which of the following is an even function?

g(x) = (x – 1)2 + 1

g(x) = 2x2 + 1

g(x) = 4x + 2

g(x) = 2x

If f(x) is an even function and (6, 8) is one the points on the graph of f(x), which reason explains why (–6, 8) must also be a point on the graph?

Since the function is even, the outputs of a negative x-value and a positive x-value are the same.

Since the function is even, the outputs of a negative y-value and a positive y-value are the same.

The graph has rotational symmetry, so the point will be reflected across the y-axis.

The graph has rotational symmetry, so the point will be rotated 90 degrees about the origin.

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

She is incorrect because systems may have only complex solutions which are not visible on a graph.

She is incorrect because the solutions may have multiplicity greater than 1.

She is correct because all solutions are intersection points of the graphs.

She is correct because the solutions are irrational.

Which statement describes how the graph of the given polynomial would change if the term –3x6 is added?y = 2x6 + 9x5 – 7x3 – 1

Both ends of the graph will approach negative infinity.

The ends of the graph will extend in opposite directions.

Both ends of the graph will approach positive infinity.

The ends of the graph will approach zero.

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