D
given the equation of a parabola in standard form : ax² + bx + c = 0 ( a ≠ 0 )
then the x-coordinate of the vertex = - [tex]\frac{b}{2a}[/tex]
y = - 2x² + 4x + 12 is in standard form
with a = - 2, b= 4 and c = 12
[tex]x_{vertex}[/tex] = - [tex]\frac{4}{-4}[/tex] = 1
substitute x = 1 into the equation for y
y = - 2(1)² + 4(1) + 12 = 14
vertex = (1, 14 )