The formula in order to obtain the vertex form of a quadratic equation is given as
y=a(x-h)^2+k where (h,k) is the vertex of the quadratic equation which is parabolic in shape and it is opening upward.
As given in the problem, y=6x^2+12x-10
Using the formula, we can transformed the quadratic equation y=6x^2+12x-10 into its vertex form:
y=6x^2+12x-10
y= (6x^2+12x)-10 (grouping)
y=6(x^2+2x)-10 (factoring Common terms per group)
y=6(x^2+2x+1)-10-6 (Completing the squares)
y=6(x+1)^2-16 (Factor and Simplify)
Hence, the vertex form of y=6x^2+12x-10 is y=6(x+1)^2-16