2
advanced-math

Convert y=2(x−1)2+3y = 2(x - 1)^2 + 3 to standard form.

A

y=2x2−4x+5y = 2x^2 - 4x + 5

B

y=2x2−2x+5y = 2x^2 - 2x + 5

C

y=2x2−4x+4y = 2x^2 - 4x + 4

D

y=2x2+5y = 2x^2 + 5

Correct Answer: A

Choice A is the correct answer. Follow the order of operations (PEMDAS): Exponents first, then Multiplication, then Addition.

  1. Expand: (x−1)2=x2−2x+1(x - 1)^2 = x^2 - 2x + 1.
  2. Distribute: 2(x2−2x+1)=2x2−4x+22(x^2 - 2x + 1) = 2x^2 - 4x + 2.
  3. Add: (2x2−4x+2)+3=2x2−4x+5(2x^2 - 4x + 2) + 3 = 2x^2 - 4x + 5.

Choice B is incorrect because it forgets to distribute the 2 to the middle term (−2x-2x). Choice C is incorrect because 2+3=52+3=5, not 4. Choice D is incorrect because it ignores the middle term entirely.

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