Write the quadratic function in the form g(x)= a (x-h)^2 +k . then, give the vertex of its graph. g(x)=3x^2+30x+72
writing in the form specified: g(x)=
vertex:

So hmmm as you may know by now...  

is a perfect square trinomial

now, let's take a closer look at the middle guy
is just 2 * guy on the left * guy on the right
so the middle term is just the product of the  two terms of the binomial, without the exponent, or square rooted, and 2

alrite... that said.... now let's do some grouping



so hmm we're missing the guy on the right there... who may that be?

well, we know the middle term is 10x, wait a minute, 10x is just 2 * 5 * x

so, if the guy on the left is "x", the other guy must be "5", 2*5*x = 10x

now, what we do is, we add 5²

however, bear in mind that, all we're doing is, borrowing from our very good friend Mr Zero, 0

so, if we add 5², we also have to subtract 5², so +5² - 5²

let's do so