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Set 8: Quadratic Equations (Intermediate)

Explanation

Answer: A

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

A.

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

✓ Correct
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

Detailed Explanation

Choice A is correct. 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 - 6 x + 9. 2. Add the constant term: (x26x+9)+2(x^2 - 6 x + 9) + 2. 3. Combine like terms: x26x+11x^2 - 6 x + 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-6 x. Choice D is incorrect because the middle term is 2(3)x=6x-2(3)x = -6 x.

Key Steps:

The correct answer is y=x26x+11y = x^2 - 6x + 11

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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