9
advanced-math

Write the equation for a parabola with vertex (2,−3)(2, -3) and a=1a = 1.

A

y=(x−2)2−3y = (x - 2)^2 - 3

B

y=(x+2)2−3y = (x + 2)^2 - 3

C

y=(x−2)2+3y = (x - 2)^2 + 3

D

y=x2−2x−3y = x^2 - 2x - 3

Correct Answer: A

Choice A is the correct answer. Use vertex form y=a(x−h)2+ky = a(x - h)^2 + k.

  1. Substitute h=2h=2, k=−3k=-3, and a=1a=1.
  2. y=1(x−2)2+(−3)y = 1(x - 2)^2 + (-3).
  3. Simplify: y=(x−2)2−3y = (x - 2)^2 - 3.

Choice B is incorrect because it uses h=−2h=-2. Choice C is incorrect because it uses k=3k=3. Choice D is incorrect because it is not the correct standard form expansion.

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Set 7: Quadratic Equations and Functions 7