I really don't mean to be a nusance, I am new here and hope to be more of a contributer of this site rather that bothering people, so I apologize. I seem to have a hard time with a specific step in taking a quadratic trinomial that cannot be factored and and converting it into a vertex formula [f(x)=(x-h)²+k].
In this case:
f(x)= 2x² + 8x + 7
I know that the first step is to group the x terms leaving the leading coefficient out of the parenthesis such as:
f(x)= 2(x² + 4x) + 7
Next step is to take the middle term and square half the coefficient: (4/2)² and then add and subtract by that number.
f(x)= 2(x² + 4x+4-4) + 7
Now here is where it gets fuzzy for me, I read this online and here is the further step according to what I read:
Now, move the second -4 to the outside of the parenthesis, only now we have to consider that the outside coefficient isn't just a simple positive one. There's a 2 out there.
f(x) = 2(x² + 4x + 4) - 2(4) + 7
Question, is that -2 that is underlined the -4 that was outside the parentesis? And if so where did that four to the right of it come from? I'm stumped as to how it got there because if the -2 was the -4 inside the parenthesis and we have the +4 inside the parenthesis, that (4) that is next to the -2 seems to have crashed the party. I just can't figure out how it got there according to there steps and there seems to be no sufficient information as to how it got there, please explain.