Find the coordinates of the vertex of the parabola y = -x ^ 2 + 2x-14

General form of the equation: a * x ^ 2 – b * x – c. In this case, the x coordinate of the vertex of the parabola is found by the formula:

x = (-b) / (2 * a).

Coefficient values: a = -1, b = 2, c = -14.

Let’s substitute the coefficients in the formula:

x = (-2) / (2 * (-1)) = -2 / (-2) = 1.

To determine the y coordinate, we substitute the found value of the x coordinate into the original function:

y = – (1) ^2 + 2 * 1 – 14 = -1 + 2 – 14 = 1 – 14 = -13.

Answer: the coordinates of the vertex of the parabola are (1; -13).