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advanced-math

Find the intersection points of y=x2y = x^2 and y=x+2y = x + 2.

A

(2,4)(2, 4) and (−1,1)(-1, 1)

B

(2,2)(2, 2) and (−1,−1)(-1, -1)

C

(1,1)(1, 1) and (−2,4)(-2, 4)

D

(0,0)(0, 0) and (2,4)(2, 4)

Correct Answer: A

Choice A is the correct answer. To find intersection points, set the equations equal to each other.

  1. x2=x+2x^2 = x + 2.
  2. Rearrange: x2−x−2=0x^2 - x - 2 = 0.
  3. Factor: (x−2)(x+1)=0(x - 2)(x + 1) = 0.
  4. Roots: x=2x = 2 and x=−1x = -1.
  5. Find y-values:
    • If x=2,y=22=4x=2, y=2^2=4. Point (2,4)(2, 4).
    • If x=−1,y=(−1)2=1x=-1, y=(-1)^2=1. Point (−1,1)(-1, 1).

Choice B is incorrect because y-values are wrong. Choice C is incorrect because x-values are swapped/wrong. Choice D is incorrect because (0,0)(0,0) is not on the line.

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Set 13: Quadratic Equations and Functions 13