2
advanced-math

Find the intersection of y=x2y = x^2 and y=−x2+8y = -x^2 + 8.

A

(2,4)(2, 4) and (−2,4)(-2, 4)

B

(2,4)(2, 4) only

C

(4,16)(4, 16) and (−4,16)(-4, 16)

D

No intersection

Correct Answer: A

Choice A is the correct answer.

  1. Set equal: x2=−x2+8x^2 = -x^2 + 8.
  2. 2x2=82x^2 = 8.
  3. x2=4⇒x=±2x^2 = 4 \Rightarrow x = \pm 2.
  4. Substitute back: y=(2)2=4y = (2)^2 = 4 and y=(−2)2=4y = (-2)^2 = 4.
  5. Points: (2,4)(2, 4) and (−2,4)(-2, 4).

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

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Set 15: Quadratic Equations and Functions 15