Systems of Inequalities — Quiz

Question 6 • Algebra 2

Which graph represents the solution of y is less than or equal to x squared minus 1 and x is greater than y squared minus 3 ?

Answer

Image with description On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens up and goes through (negative 2, 3), has vertex (0, negative 1), and goes through (2, 3). Everything inside of the first parabola and outside of the second parabola is shaded.

Image with description On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens down and goes through (2, negative 5), has vertex (0, negative 1), and goes through (2, negative 5). Everything inside of the first parabola and outside of the second parabola is shaded.

Image with description On a coordinate plane, a parabola opens to the right and goes through (6, 3), has vertex (negative 3, 0), and goes through (6, negative 3). Another parabola opens down and goes through (2, negative 5), has vertex (0, negative 1), and goes through (2, negative 5). Everything inside of the first parabola and second parabola is shaded.

Explanation

The inequality x > y² − 3 rearranges to y² < x + 3, so the solution lies inside the right-opening parabola with vertex (−3, 0). The inequality y ≤ x² − 1 places the solution on or below the upward-opening parabola with vertex (0, −1), which is outside the region enclosed by that parabola. Choice A shades inside the right-opening parabola and outside the upward-opening parabola.

AI-written and checked against the verified answer.

More from this Course

Pretest

Test

Test