F(x) = 2x2 + 12x + 1
Determine the vertex

Step-by-step explanation:

The vertex would be the highest/lowest point so lets factor this first

when we factor we get

2(x^2+6x+8)

2(x+4) (x+2)

Using zero product property we find the 2 x values and x intercepts are

-4 and -2

the middle point of these points is -3

Substitute -3 for x and solve

2(-3+4) (-3+2)

2 * 1 *  -1

2*-1

-2

(-3,-2) is the vertex