3

Set 7: Quadratic Equations

Explanation

Answer: A

Profit P(x)P(x) from selling xx items is P(x)=−x2+200x−1000P(x) = -x^2 + 200x - 1000. How many items must be sold to maximize profit?

A.

100

✓ Correct
B.

200

C.

50

D.

1000

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Find the x-coordinate of the vertex. 1. x=−b/2ax = -b/2 a. 2. x=−200/(2(−1))=−200/−2=100x = -200 / (2(-1)) = -200 / -2 = 100. 3. Selling 100 items maximizes profit. Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is 100

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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