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Set 10: Quadratic Equations (Intermediate)

Explanation

Answer: A

Which function has a maximum value?

A.

y=2x2+4xy = -2x^2 + 4x

✓ Correct
B.

y=x25y = x^2 - 5

C.

y=3(x1)2y = 3(x-1)^2

D.

y=0.5x2+2y = 0.5x^2 + 2

Detailed Explanation

Choice A is correct. Choice A is the correct answer. A quadratic function has a maximum value only if it opens downward. 1. Check the leading coefficient aa for each option. 2. A: a=2a = -2 (Negative \rightarrow Opens Down \rightarrow Maximum). 3. B: a=1a = 1 (Positive \rightarrow Opens Up \rightarrow Minimum). 4. C: a=3a = 3 (Positive). 5. D: a=0.5a = 0.5 (Positive). Choice B is incorrect because a>0a > 0. Choice C is incorrect because a>0a > 0. Choice D is incorrect because a>0a > 0.

Key Steps:

The correct answer is y=2x2+4xy = -2x^2 + 4x

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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