Set 9: Quadratic Equations (Advanced)

Explanation

Answer: A

If the vertex of a parabola is $(3, 5)$ and it opens upward, what is the range of the function?

$y \geq 5$

✓ Correct

$y \leq 5$

$y \geq 3$

All real numbers

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. The vertex is $(3, 5)$ , so the minimum y-value is 5. 2. Since it opens upward, the graph goes up to infinity from 5. 3. Therefore, the range is all y-values greater than or equal to 5 ( $y \geq 5$ ). Choice B is incorrect because that would be for a parabola opening downward. Choice C is incorrect because it uses the x-coordinate. Choice D is incorrect because the range of a quadratic is never all real numbers (the domain is).

Key Steps:

•

The correct answer is $y \geq 5$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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