Question

The vertex of the parabola \( 4y = x^2 - 6x + 17 \) is

• A. \( (3,2) \)
• B. \( (4,3) \)
• C. \( (4,2) \)
• D. \( (3,7) \)
• E. \( (7,2) \)

Hint:

Vertex form comes after completing square: \( y = a(x-h)^2 + k \Rightarrow (h,k) \).

Answer 1

The Correct Option is A

Concept: Complete square to find vertex.

Step 1: Rewrite equation.
\[ 4y = x^2 - 6x + 17 \]

Step 2: Complete square.
\[ x^2 - 6x = (x-3)^2 - 9 \] \[ 4y = (x-3)^2 - 9 + 17 = (x-3)^2 + 8 \] \[ y = \frac{(x-3)^2}{4} + 2 \]

Step 3: Identify vertex.
\[ (3,2) \]