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 :)

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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) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-36x-117 Start with the right side of the given equation.


3%28x%5E2-12x-39%29 Factor out the x%5E2 coefficient 3. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient -12 to get -6. In other words, %281%2F2%29%28-12%29=-6.


Now square -6 to get 36. In other words, %28-6%29%5E2=%28-6%29%28-6%29=36


3%28x%5E2-12x%2Bhighlight%2836-36%29-39%29 Now add and subtract 36 inside the parenthesis. Make sure to place this after the "x" term. Notice how 36-36=0. So the expression is not changed.


3%28%28x%5E2-12x%2B36%29-36-39%29 Group the first three terms.


3%28%28x-6%29%5E2-36-39%29 Factor x%5E2-12x%2B36 to get %28x-6%29%5E2.


3%28%28x-6%29%5E2-75%29 Combine like terms.


3%28x-6%29%5E2%2B3%28-75%29 Distribute.


3%28x-6%29%5E2-225 Multiply.


So after completing the square, 3x%5E2-36x-117 transforms to 3%28x-6%29%5E2-225. So 3x%5E2-36x-117=3%28x-6%29%5E2-225.


So y=3x%5E2-36x-117 is equivalent to y=3%28x-6%29%5E2-225.


Now y=3%28x-6%29%5E2-225 is in vertex form y=a%28x-h%29%5E2%2Bk where (h,k) is the vertex. In this case, h=6 and k=-225. 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 3%28x-6%29%5E2-225 to get the original expression again.