AnswersAlgebra 2Systems — TestQuestion 15
15
QuizMultiple Choice

Systems — Test

Question 15 • Algebra 2

Which graph represents the solution of y is less than or equal to x squared plus 1 and x is greater than y squared minus 5 ?

Answer
A
Image with description On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 1) and goes through (2, 6). Another parabola opens to the right and goes through (4, 3), has vertex (negative 5, 0), and goes through (4, negative 3). Everything inside of both parabolas is shaded.
B
Image with description A right-opening dashed parabola has a vertex at left-parenthesis negative 5 comma 0 right-parenthesis and passes through left-parenthesis 4 comma 3 right-parenthesis and left-parenthesis 4 comma negative 3 right-parenthesis. An upward-opening solid parabola has a vertex at left-parenthesis 0 comma 1 right-parenthesis and passes through left-parenthesis negative 2 comma 6 right-parenthesis and left-parenthesis 2 comma 6 right-parenthesis. The region outside the parabolas is shaded one color. The region inside the dashed parabola is shaded a second color. The regions where the two parabolas overlap is shaded a third color.
C
Image with description On a coordinate plane, a parabola opens up and goes through (negative 3, 4), has vertex (0, negative 5), and goes through (3, 4). Another parabola opens to the right and goes through (5, 2), has vertex (1, 0), and goes through (5, negative 2). Everything inside of both parabolas is shaded.
D
Image with description On a coordinate plane, a parabola opens up and goes through (negative 3, 4), has vertex (0, negative 5), and goes through (3, 4). Another parabola opens to the right and goes through (5, 2), has vertex (1, 0), and goes through (5, negative 2). Everything inside the first parabola and outside of the second parabola is shaded.

Explanation

The boundary y = x² + 1 is an upward-opening parabola with vertex (0, 1); because the inequality is ≤, its boundary is solid and the region below it is included. The boundary x = y² − 5 opens to the right and has vertex (−5, 0); because the inequality is strict (>), its boundary is dashed, and the solution lies to its right. Choice B shows both boundaries correctly and marks the overlap of the two solution regions.

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