4
advanced-math

Find the break-even points (where Profit = 0) for P(x)=−x2+50x−400P(x) = -x^2 + 50x - 400.

A

10 and 40

B

20 and 30

C

5 and 80

D

0 and 50

Correct Answer: A

Choice A is the correct answer. Solve P(x)=0P(x) = 0.

  1. −x2+50x−400=0-x^2 + 50x - 400 = 0.
  2. Multiply by -1: x2−50x+400=0x^2 - 50x + 400 = 0.
  3. Factor: (x−10)(x−40)=0(x - 10)(x - 40) = 0.
  4. Break-even points are 10 and 40 units.

Choice B is incorrect. Choice C is incorrect. Choice D is incorrect.

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Set 18: Quadratic Equations and Functions 18