8
advanced-math

Convert y=(x3)2+2y = (x - 3)^2 + 2 to standard form.

A

y=x26x+11y = x^2 - 6x + 11

B

y=x26x+5y = x^2 - 6x + 5

C

y=x2+9+2y = x^2 + 9 + 2

D

y=x23x+5y = x^2 - 3x + 5

Correct Answer: A

Choice A is the correct answer. To convert from vertex form to standard form:

  1. Expand the squared binomial: (x3)2=x26x+9(x - 3)^2 = x^2 - 6x + 9.
  2. Add the constant term: (x26x+9)+2(x^2 - 6x + 9) + 2.
  3. Combine like terms: x26x+11x^2 - 6x + 11.

Choice B is incorrect because it likely subtracted 2 instead of adding, or calculated 949-4. Choice C is incorrect because it misses the middle term 6x-6x. Choice D is incorrect because the middle term is 2(3)x=6x-2(3)x = -6x.