Answers MO-Algebra II AMixed Degree Systems

Mixed Degree Systems Answers

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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?

The parabola opens downward.

The parabola opens upward.

The slope of the line is equal to –1.

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

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What are the solutions of the following system?

(0, –5) and (–5, 5)

(0, –5) and (5, –15)

(0, –5) and (–4, 3)

(0, –5) and (4, –13)

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

zero

one

two

three

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?

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.

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.

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.

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.

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?

The maximum number of solutions is one.

The maximum number of solutions is three.

The circle has a radius equal to 3.

The circle has a radius less than 9.

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?

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?

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

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

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

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

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

Each graph has one y-intercept, which is a solution.

Each graph has one vertex, which is a solution.

The graphs of the equations intersect the x-axis at two places.

The graphs of the equations intersect each other at two places.

What are the solutions to the following system?

(0, 2)

(1, –2)

and

and

What are the solutions of the following system?

and

and

(6, 312) and (–6, 312)

(6, 312) and (–6, –264)

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

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

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

The equations represent parabolas that result in the same graph.

The equations represent circles that result in the same graph.

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

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

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

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

Which equation is part of solving the system by substitution?

4(y + 11)2 – 3y2 = 8

4(11 – y)2 – 3y2 = 8

4(y – 11)2 – 3y2 = 8

4(–11y)2 – 3y2 = 8

Which graph represents the solution of the system ?

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).

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).

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).

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).

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

zero

one

two

three

What are the solutions of the following system?

(0, –5) and (–5, 5)

(0, –5) and (5, –15)

(0, –5) and (–4, 3)

(0, –5) and (4, –13)

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

one

two

three

four

Which graph shows a system of equations with no solutions?

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.

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.

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

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.

Which system is equivalent to ?

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

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

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

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

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.

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.

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.

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.

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Mixed Degree Systems Answers

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