SOLUTION: Hello I was wondering if you could help me answer this problem. converting to vertex form y=3x^2-36x-117 thank you for your help :)

Question 219646: Hello I was wondering if you could help me answer this problem.
converting to vertex form
y=3x^2-36x-117
thank you for your help :)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the right side of the given equation.

Factor out the coefficient . This step is very important: the coefficient must be equal to 1.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

Distribute.

Multiply.

So after completing the square, transforms to . So .

So is equivalent to .

Now is in vertex form where (h,k) is the vertex. In this case, and . So the vertex is (6, -225).

Note: to verify the answer, you could either graph the two equations (and you'll see that they are really the same) or you can expand out to get the original expression again.

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