Question

which is the vertex of $f(x) = 2x^2 - 8x + 11$?
a $(-2, 3)$
b $(4, 11)$
c $(-2, 36)$
d $(2, 3)$
e none of these
f $(2, 9)$

Explanation:

Step1: Find x-coordinate of vertex

For a quadratic function \( f(x) = ax^2 + bx + c \), the x-coordinate of the vertex is given by \( x = -\frac{b}{2a} \). Here, \( a = 2 \), \( b = -8 \). So, \( x = -\frac{-8}{2\times2} = \frac{8}{4} = 2 \).

Step2: Find y-coordinate of vertex

Substitute \( x = 2 \) into \( f(x) = 2x^2 - 8x + 11 \). \( f(2) = 2(2)^2 - 8(2) + 11 = 2\times4 - 16 + 11 = 8 - 16 + 11 = 3 \). So the vertex is \( (2, 3) \), which is option D.

Answer:

D. (2, 3)