Question 269455
step 1 - factor out the 3 from the first 2 terms to get
{{{y = 3(x^2 - 8x) + 43}}}
step 2 - draw lines after the -8x and the 43. These are number holders. numbers will go here.
{{{y = 3(x^2 - 8x + _____) + 43 + _____ }}}
step 3 - take 1/2 of the -8 and square it to get (-4)^2. Put this in the parenthesis to get
{{{y = 3(x^2 - 8x + (-4)^2) + 43 + _____ }}}
step 4 - you have put 16 into the (__) information, but there is a 3 on the outside. Multiply 3 by 16 to get 48. We have just added 48 to the right. To keep it all balanced, put -48 in the outside blank space. We get
{{{y = 3(x^2 - 8x + (-4)^2) + 43 + -48 }}}
step 5 - rewrite the trinomial as a binomial squared and simplify the outside numbers as
{{{y = 3(x -4)^2 -5 }}}
step 6 state vertex as
(h,k) = (4,-5)