For the parabola

y = ax^2 + bx + c

The x value of the vertex is given by

x = -b/(2a)

For your parabola, this is

x = -(12)/(2*(-2)) = 3

The value of y at that point is

y = -2(3^2) + 12(3) - 13

= -2*9 + 36 - 13

= 5

y = ax^2 + bx + c

The x value of the vertex is given by

x = -b/(2a)

For your parabola, this is

x = -(12)/(2*(-2)) = 3

The value of y at that point is

y = -2(3^2) + 12(3) - 13

= -2*9 + 36 - 13

= 5

**The vertex is located at (x, y) = (3, 5).**