Answers NY-Algebra II Term 2 HillcrestMixed Degree Systems

Mixed Degree Systems Answers

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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

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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.

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.

What are the solutions to the following system?

(0, 2)

(1, –2)

and

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?

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.

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

one

two

three

four

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.

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

zero

one

two

three

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

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