Question 744661

The vertex form of a parabola's equation is generally expressed as :
{{{y= a(x-h)^2+k}}}

given:

{{{y = 3x ^2 - 30x - 7}}}...factor out {{{3}}} from first two terms

{{{y = 3(x ^2 - 10x) - 7}}}.......complete square {{{(x ^2 - 10x+____)}}}, add 25 to {{{(x ^2 - 10x+____)}}}, then subtract {{{3*25}}} from {{{3(x ^2 - 10x+____)}}}

{{{y = 3(x ^2 - 10x+25)-3*25 - 7}}}

{{{y=3(x^2-10x+25)-82}}}

{{{y=3(x-5)^2-82}}}.......vertex form