Find the vertex of this parabola.

y = -2x2 + 4x + 12

a.
(-4, 12)

b.
(-2, 6)

c.
(3, 6)

d.
(1, 14)

The vertex of this parabola is (1, 14).

Step-by-step explanation:

To find the vertex of this parabola, one approach is to determine the equation of the axis of symmetry:  evaluate x = -b / (2a), where a, b and c are the coefficients of the x^2, x and x^0 terms respectively.

Here a = -2, b = 4 and c = 12.

Thus, the axis of symmetry is x = -4 / (2· -2), or x = 1.

The function value at x = 1 is   y = -2(1)^2 + 4(1) + 12, or  y = -2 + 4 + 12 = 14.

The vertex of this parabola is (1, 14).