Mixed Degree Systems Answers

1

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Consider the following system of equations.Which statement describes why the system has infinite solutions?

A

The equations represent parabolas that result in graphs that do not intersect.

B

The equations represent circles that result in graphs that do not intersect.

C

The equations represent parabolas that result in the same graph.

D

The equations represent circles that result in the same graph.

2

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Which graph shows a system of equations with no solutions?

A

On a coordinate plane, the graphs of 2 circles are shown. Both circles have a center at (0, 0). The smaller circle is within the larger circle and the smaller circle has a radius that is 2 units smaller than the larger circle.

B

On a coordinate plane, a graph of a line and a parabola are shown. The line is horizontal to the x-axis at y = negative 5. The parabola opens up and its vertex on the line.

C

On a coordinate plane, the graphs of 2 circles are shown. Both circles are in quadrant 1, and they intersect each other.

D

On a coordinate plane, the graphs of 2 parabolas are shown. Both parabolas open up and they intersect each other at (0, 0). The first parabola has a vertex in quadrant 3 and the second parabola has a vertex in quadrant 4.

3

What are the solutions of the following system?

A

(0, –5) and (–5, 5)

B

(0, –5) and (5, –15)

C

(0, –5) and (–4, 3)

D

(0, –5) and (4, –13)

4

The center of a circle is at the origin on a coordinate grid. The vertex of a parabola that opens upward is at (0, 9). If the circle intersects the parabola at the parabola’s vertex, which statement must be true?

A

The maximum number of solutions is one.

B

The maximum number of solutions is three.

C

The circle has a radius equal to 3.

D

The circle has a radius less than 9.

5

Which graph represents the solution of the system ?

A

On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 4 units. The line has a negative slope and goes through (negative 3, 4), (0, 1), and (1, 0).

B

On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 2 units. The line has a positive slope and goes through (negative 3, negative 4), (0, negative 1), and (1, 0).

C

On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 4 units. The line has a positive slope and goes through (negative 3, negative 4), (0, negative 1), and (1, 0).

D

On a coordinate plane, a graph of a circle and a straight line are shown. The circle has a center at (0, 0) and a radius of 2 units. The line has a negative slope and goes through (negative 3, 4), (0, 1), and (1, 0).

6

The vertex of a parabola is in the first quadrant of a coordinate grid. A line with a negative slope passes through the origin. If the parabola and line intersect at the origin, which statement must be true?

A

The parabola opens downward.

B

The parabola opens upward.

C

The slope of the line is equal to –1.

D

The slope of the line is not equal to –1.

7

Parabola A can be represented using the equation (x + 3)2 = y, while line B can be represented using the equation y = mx + 9. Isabel claims one solution to the system of two equations must always be the vertex of parabola A. Which best describes the reasonableness of her claim?

A

Isabel is correct because the y-intercept of line B is (0, 9) and the value of y when x = 0 in parabola A is 9.

B

Isabel is correct because the y-intercept of line B is (9, 0) and the value of x when y = 0 in parabola A is 9.

C

Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.

D

Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the x-intercept of the equations, not the vertex.

8

Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola. Equation 1: (x – 3)2 = y – 4 Equation 2: y = -x + bIn order for Tom’s thinking to be correct, which qualifications must be met?

A

b must equal 7 and a second solution to the system must be located at the point (2, 5).

B

b must equal 1 and a second solution to the system must be located at the point (4, 5).

C

b must equal 7 and a second solution to the system must be located at the point (1, 8).

D

b must equal 1 and a second solution to the system must be located at the point (3, 4).

9

Which system is equivalent to ?

A

StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 2 2nd row x = y minus 2 EndLayout

B

StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 2 2nd row x = y + 2 EndLayout

C

StartLayout Enlarged left-brace 1st row y = negative 2 y squared minus 8 y minus 8 2nd row x = y + 2 EndLayout

D

StartLayout Enlarged left-brace 1st row y = negative 2 y squared + 8 y minus 8 2nd row x = y minus 2 EndLayout

10

Pablo graphs a system of equations. One equation is quadratic and the other equation is linear. What is the greatest number of possible solutions to this system?

A

0

B

1

C

2

D

4

11

How many solutions exist for the mixed-degree system graphed below?

A

zero

B

one

C

two

D

three

12

Which graph shows the system ?

A

On a coordinate plane, a graph of a circle and a parabola are shown. The circle has a center at (0, 0) and a radius of 3 units. The parabola opens down and intersects the circle at (negative 2, negative 2), has a vertex at (0, 2), and intersect the circle again at (2, negative 2).

B

On a coordinate plane, a graph of a circle and a parabola are shown. The circle has a center at (0, 0) and a radius of 3 units. The parabola opens up and intersects the circle at (negative 2, 2), has a vertex at (0, negative 2), and intersect the circle again at (2, 2).

C

On a coordinate plane, a graph of a circle and a parabola are shown. The circle has a center at (0, 3) and has a radius of 3 units. The parabola opens up and intersects the circle at (negative 2, 5), has a vertex at (0, 2), and intersects the circle again at (2, 5).

D

On a coordinate plane, a graph of a circle and a parabola are shown. The circle has a center at (0, 3) and has a radius of 3 units. The parabola opens down and goes through (negative 2, negative 2), has a vertex at (0, 2), and goes through (2, negative 2).

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