Precalculus help

Question

If y=3x^2 + 12x - 3 is put in the form y=a(x-h)^2+k, then what is the value of (a+h+k)?

Answer 1

They are asking you to complete the square in this question, you do this by taking half the number in from of x and then squaring it (half down, square up), but first we need to pull out the 3:

3(x²+4x-1), now we half down square up: 4/2=2, 2²=4, to keep this equation even we add and subtract 4:

3(x²+4x+4-1-4)=3((x²+4x+4)-5), now lets factor the middle equation and pull out the -5:

3(x+2)²-15 now we can do a+h+k which is 3-2-15=-14 (if you don't understand why the 2 is negative, look at the original equation/ the form they wanted and see if you can figure out why I did -2 instead of +2)

hint: -(-2)=2