9
advanced-math

The range of y=x2y = x^2 is y≥0y \geq 0. What is the range of y=−x2−3y = -x^2 - 3?

A

y≤−3y \leq -3

B

y≥−3y \geq -3

C

y≤0y \leq 0

D

y≥3y \geq 3

Correct Answer: A

Choice A is the correct answer.

  1. Vertex: (0,−3)(0, -3).
  2. Direction: Opens downward (a=−1a=-1).
  3. Range: Since it opens down, the vertex is the maximum. All y-values must be less than or equal to the vertex y-coordinate.

So, y≤−3y \leq -3.

Choice B is incorrect because it opens downward. Choice C is incorrect because the vertex is at -3. Choice D is incorrect because it opens downward and vertex is at -3.

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Set 9: Quadratic Equations and Functions 9