Question

find the vertex.

f(x) = 3x² + 6x − 11

(?, )

Explanation:

Step1: Find x-coordinate of vertex

For quadratic $ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=3, b=6$:
$x=-\frac{6}{2\times3}=-1$

Step2: Find y-coordinate of vertex

Substitute $x=-1$ into $f(x)$:
$f(-1)=3(-1)^2+6(-1)-11=3-6-11=-14$

Answer:

$(-1, -14)$