Advanced Math practice question

Answer: A. 3

For f(x) = ax² + bx + c, the vertex has x-coordinate −b/(2a). Here a = 1 and b = −6, so x = −(−6)/(2·1) = 6/2 = 3. (Equivalently, complete the square: x² − 6x + 1 = (x − 3)² − 8, vertex at x = 3.)

Why the other answers are wrong

B. −3

The sign was dropped: −b/(2a) with b = −6 is −(−6)/2 = +3. Two negatives make a positive.

C. 6

6 is −b, but you still have to divide by 2a = 2. The vertex sits halfway between the roots, not at −b itself.

D. −6

−6 is just b read off the equation. The formula is −b divided by 2a, which changes both the sign and the size.

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