8
advanced-math

Find the minimum vertical distance between the parabolas y=x2+4y = x^2 + 4 and y=−x2y = -x^2.

A

4

B

0

C

2

D

8

Correct Answer: A

Choice A is the correct answer. Vertical distance is the difference in y-values.

  1. D(x)=(x2+4)−(−x2)=2x2+4D(x) = (x^2 + 4) - (-x^2) = 2x^2 + 4.
  2. This is a parabola opening upward.
  3. The minimum value occurs at the vertex (x=0x=0).
  4. Min Distance =2(0)2+4=4= 2(0)^2 + 4 = 4.

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

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Set 20: Quadratic Equations and Functions 20