What is the focus of the parabola?

y=-14x2-2x-2

First, we need to transform the equation into its standard form (x - h) ²=4p (y - k).

Using completing the square method:

y = - 14x² - 2x - 2

y = - 14 (x² + 2x/14) - 2

y = - 14 (x² + 2x/14 + (2/28) ²) - 2 + (2/28) ²

y = - 14 (x + 1/14) ² - 391/196

-1/14 (y + 391/196) = (x + 1/14) ²

This is a vertical parabola and its focus (h, k + p) is (-1/14, - 391/196 + 1/56) = (-1/14, - 775/392).

Or (-0.071,-1.977).