What is the vertex of the parabola y equals -2x squared plus 12x -13?

There are two forms in which a quadratic equation can be written: general form, which is ax2 + bx + c, and standard form, which is a(x - q)2 + p. In standard form, the vertex is (q, p). So to find the vertex, simply convert general form into standard form.

The formula often used to convert between these two forms is:

ax2 + bx + c = a(x + b/2a)2 + c - b2/4a

Substitute the variables:

-2x2 + 12x - 13 = -2(x + 12/-4)2 -13 + 122/-8

-2x2 + 12x - 13 = -2(x - 3)2 + 5

Since the co-ordinates of the vertex are equal to (q, p), the vertex of the parabola defined by the equation y = -2x2 + 12x - 13 is located at point (3, 5)