Write y = x^2 - 6x + 8 in vertex form.

• A. y = (x - 3)^2 - 1
• B. y = (x + 3)^2 - 1
• C. y = (x - 3)^2 + 1
• D. y = x^2 - 6x - 2

Answer: (A)

Converting a quadratic to vertex form means writing it as y = a(x − h)^2 + k, which makes the vertex (h, k) clear. Here a is 1 because the x^2 coefficient is 1. To find h, look at the x-term: −6x comes from expanding (x − h)^2 = x^2 − 2hx + h^2, so −2h = −6 gives h = 3. Then complete the square to find k: y = x^2 − 6x + 8 = (x^2 − 6x + 9) − 9 + 8 = (x − 3)^2 − 1. Thus the vertex form is y = (x − 3)^2 − 1, with the vertex at (3, −1) and the parabola opening upward.