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advanced-math

Find the axis of symmetry for the parabola y=x24x+7y = x^2 - 4x + 7.

A

x=2x = 2

B

x=2x = -2

C

x=4x = 4

D

x=4x = -4

Correct Answer: A

Choice A is the correct answer. The axis of symmetry for a quadratic function y=ax2+bx+cy = ax^2 + bx + c is the vertical line given by the formula x=b2ax = -\frac{b}{2a}.

  1. Identify coefficients: a=1a = 1, b=4b = -4.
  2. Substitute into formula: x=42(1)x = -\frac{-4}{2(1)}.
  3. Simplify: x=42=2x = \frac{4}{2} = 2.

Choice B is incorrect because of a sign error (forgot the negative in the formula). Choice C is incorrect because it forgets to divide by 2. Choice D is incorrect because of both errors.