Completing the square is used to turn a regular standard form equation into a vertex form. Completing the square is useful when graphing a parabola because it is easy to graph it from vertex form. To turn a standard form equation (y= ax^2 + bx + c) to vertex form (y= a(x-h)^2=k) you have to complete the square.
Here is how you complete the square: y=-2x^2+8x+7 y=-2(x^2-4)+7 y=-2(x-2)^2+7 y=-2(x-2)^2+15