Advanced Math practice question

Answer: A. (3, 5)

In vertex form f(x) = (x − h)² + k, the vertex is (h, k). Here h = 3 and k = 5, so the vertex is (3, 5). Check: f(3) = 0 + 5 = 5, and any other x adds a positive square, so 5 is the minimum.

Why the other answers are wrong

B. (−3, 5)

The sign of h is easy to flip: (x − 3)² is zero when x = 3, not x = −3. The vertex form subtracts h, so 'x − 3' means h = +3.

C. (3, −5)

The +5 sits outside the square and is added as-is, so k = 5, not −5.

D. (−3, −5)

Both signs were flipped. Read vertex form as (x − h)² + k: h is what makes the bracket zero, and k is the constant added on.

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