Question

find the vertex of the following quadratic
y = 2x² -12x +11
a) (3, -7)
b) (-3, 65)
c) (3, 65)
d) (0, 11)

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( y = ax^2 + bx + c \), the x - coordinate of the vertex is given by \( x=-\frac{b}{2a} \). Here, \( a = 2 \) and \( b=- 12 \).
So, \( x =-\frac{-12}{2\times2}=\frac{12}{4} = 3 \).

Step2: Find y - coordinate of vertex

Substitute \( x = 3 \) into the equation \( y=2x^{2}-12x + 11 \).
\( y=2\times(3)^{2}-12\times3 + 11=2\times9-36 + 11=18-36 + 11=-7 \).

So the vertex is \( (3,-7) \).

Answer:

A. (3, -7)