7
advanced-math

If the vertex of y=x2+bx+cy = x^2 + bx + c is (2,−3)(2, -3), find bb and cc.

A

b=−4,c=1b = -4, c = 1

B

b=4,c=1b = 4, c = 1

C

b=−4,c=−1b = -4, c = -1

D

b=2,c=−3b = 2, c = -3

Correct Answer: A

Choice A is the correct answer.

  1. Use vertex form: y=(x−2)2−3y = (x - 2)^2 - 3.
  2. Expand: y=x2−4x+4−3y = x^2 - 4x + 4 - 3.
  3. Simplify: y=x2−4x+1y = x^2 - 4x + 1.
  4. Compare to x2+bx+cx^2 + bx + c: b=−4,c=1b = -4, c = 1.

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

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Set 20: Quadratic Equations and Functions 20