AnswersTX-Algebra II A-CRMixed Degree Systems

Mixed Degree Systems Answers

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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.
2
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Consider the following system of equations.Which statement describes why the system has infinite solutions?

Question illustration
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.
3

Which graph represents the solution of the system ?

Question illustration
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).
Option A
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).
Option B
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).
Option C
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).
Option D
4

What are the solutions to the following system?

Question illustration
A
(0, 2)
B
(1, –2)
C
and
Option C
D
and
Option D
5

What are the solutions of the following system?

Question illustration
A
and
Option A
B
and
Option B
C
(6, 312) and (–6, 312)
D
(6, 312) and (–6, –264)
6

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

Question illustration
A
Each graph has one y-intercept, which is a solution.
B
Each graph has one vertex, which is a solution.
C
The graphs of the equations intersect the x-axis at two places.
D
The graphs of the equations intersect each other at two places.
7

What are the solutions of the following system?

Question illustration
A
(0, –5) and (–5, 5)
B
(0, –5) and (5, –15)
C
(0, –5) and (–4, 3)
D
(0, –5) and (4, –13)
8

How many solutions exist for the system of equations in the graph?

Question illustration
A
one
B
two
C
three
D
four
9

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).
10

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.

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