10
advanced-math

Find the intersection of y=x2+2xy = x^2 + 2x and y=x2+4y = x^2 + 4.

A

(2,8)(2, 8)

B

(2,6)(2, 6)

C

(−2,0)(-2, 0)

D

No intersection

Correct Answer: A

Choice A is the correct answer.

  1. Set equal: x2+2x=x2+4x^2 + 2x = x^2 + 4.
  2. Subtract x2x^2 from both sides: 2x=42x = 4.
  3. Solve: x=2x = 2.
  4. Substitute: y=22+4=8y = 2^2 + 4 = 8 (or y=22+2(2)=8y = 2^2 + 2(2) = 8).
  5. Point: (2,8)(2, 8).

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

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