Question

The coordinates of the vertex of the parabola \[ y = 2x^2 - 12x + 26 \] are

• A. \( (6,13) \)
• B. \( (3,-8) \)
• C. \( (3,8) \)
• D. \( (6,-13) \)
• E. \( (3,11) \)

Hint:

For a quadratic equation \( y = ax^2 + bx + c \), use \( x = -\frac{b}{2a} \) to find the vertex.

Answer 1

The Correct Option is C

The standard form of a quadratic equation is: \[ y = ax^2 + bx + c \] where \( a = 2 \), \( b = -12 \), and \( c = 26 \). The formula for the vertex is: \[ x = -\frac{b}{2a} \] \[ x = -\frac{-12}{2(2)} = \frac{12}{4} = 3 \] Now, substituting \( x = 3 \) in the given equation: \[ y = 2(3)^2 - 12(3) + 26 \] \[ y = 2(9) - 36 + 26 = 18 - 36 + 26 = 8 \] Thus, the vertex is \( (3,8) \). 
Final Answer: \[ \boxed{(3,8)} \]