oh wow someone please explain!?

Question

I take classes online, so its hard to get math help when i dont understand things
Find the value of "k" if f(x) = 3x2 + 6x + 1 is put into general form.

can someone please explain this?
what do i do?!

Answer 1

I think you are referring to completing the square to get the equation in vertex form:

y = a(x - h)² + k

You have:
y = 3x² + 6x + 1

Start by dividing both sides by 3 (coefficient on x²) so the coefficient on x² becomes 1.

y/3 = x² + 2x + 1/3

I also like to get the non-x terms moved out of the way, so subtract 1/3 from both sides:
y/3 - 1/3 = x² + 2x

Now you want to "complete the square". You do this by taking the coefficient on the x-term (2), dividing it in half (1) and squaring it. Add this to both sides:

y/3 - 1/3 + 1 = x² + 2x + 1
y/3 + 2/3 = x² + 2x + 1

Now the expression on the right is a perfect square, so rewrite it:
(y + 2) / 3 = (x + 1)(x + 1)
(y + 2) / 3 = (x + 1)²

You are almost there. Just undo the stuff on the left. Start by multiplying by 3:
y + 2 = 3(x + 1)²

Subtract the 2 from both sides:
y = 3(x + 1)² - 2

Comparing this to vertex form, you have a = 3, h = -1, k = -2
y = a(x - h)² + k

If you were to graph this, you would see it was an upward facing parabola (a > 0). It would be centered symmetrically around x = h = -1. The bottom of the parabola would be k = -2. In other words, the vertex of the parabola is at (-1, -2) going upward.

http://img251.imageshack.us/img251/5118/parabolatj0.gif

Answer 2

What you have to do is complete the square, like this:
f(x) = 3(x²+2x) +1
Now complete the square in brackets.
Take half the x term and add it to the expression:
3(x²+2x+1) -2 = 3(x+1)² -2. So "k" = -2.
Where did that -2 come from?
You added 3 when you completed the square
so you must subtract 2 to keep the original 1.
Hope that makes sense!