Mixed Degree Systems — Quiz

Question 8 • Advanced Algebra: Concepts and Connections

Which graph shows the following system? x squared plus y is equal to 2 x squared plus y squared is equal to 9

Answer

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 6 to 6 with an interval of 1 unit. The circle has a center at (0 comma 3) and a radius of 3 units. The parabola opens up and has a vertex at (0 comma 2), and it passes through (negative 1 comma 3), and (1 comma 3).

Image with description On a coordinate plane, the scale on the x and y axis ranges from negative 6 to 6 with an interval of 1 unit. The circle has a center at (0 comma 3) and a radius of 3 units. The parabola opens down and has a vertex at (0 comma 2), and it passes through (negative 1 comma 1), and (1 comma 1).

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 6 to 6 with an interval of 1 unit. The circle has a center at the origin and a radius of 3 units. The parabola opens down and has a vertex at (0 comma 2), and it passes through points (negative 1 comma 1), and (1 comma 1).

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 6 to 6 with an interval of 1 unit. The circle has a center at the origin and a radius of 3 units. The parabola opens up and has a vertex at (0 comma negative 2), and it passes through (1 comma negative 1), and (negative 1 comma negative 1).

Explanation

Rewrite x² + y = 2 as y = 2 − x². This parabola opens downward, has vertex (0, 2), and passes through (−1, 1) and (1, 1). The equation x² + y² = 9 is a circle centered at (0, 0) with radius 3, so choice C shows both graphs.

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