7

Set 14: Quadratic Equations (Advanced)

Explanation

Answer: A

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

A.

x=2x = 2

✓ Correct
B.

x=2x = -2

C.

x=4x = 4

D.

x=4x = -4

Detailed Explanation

Choice A is correct. 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}{2 a}. 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.

Key Steps:

The correct answer is x=2x = 2

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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