3. write the quadratic function f (x) = x2 + 6x + 14 in vertex form.

well, let's start off by doing some grouping, what we'll be doing is so-called "completing the square" as in a perfect square trinomial, since that's what the vertex form of a quadratic uses.

well, darn, we have a missing number for our perfect trinomial, however let's recall that in a perfect square trinomial the middle term is really the product of 2 times the term on the left and the term on the right without the exponent, so then we know that

well then, that's our mystery guy, now, let's recall all we're doing is borrowing from our very good friend Mr Zero, 0, so if we add 3², we also have to subtract 3².