SOLUTION: convert to vertex form y=x^2+9x+12

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Question 551125: convert to vertex form

y=x^2+9x+12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B9x%2B12 Start with the given expression.


Take half of the x coefficient 9 to get 9%2F2. In other words, %281%2F2%29%289%29=9%2F2.


Now square 9%2F2 to get 81%2F4. In other words, %289%2F2%29%5E2=%289%2F2%29%289%2F2%29=81%2F4


x%5E2%2B9x%2Bhighlight%2881%2F4-81%2F4%29%2B12 Now add and subtract 81%2F4. Make sure to place this after the "x" term. Notice how 81%2F4-81%2F4=0. So the expression is not changed.


%28x%5E2%2B9x%2B81%2F4%29-81%2F4%2B12 Group the first three terms.


%28x%2B9%2F2%29%5E2-81%2F4%2B12 Factor x%5E2%2B9x%2B81%2F4 to get %28x%2B9%2F2%29%5E2.


%28x%2B9%2F2%29%5E2-33%2F4 Combine like terms.


So after completing the square, x%5E2%2B9x%2B12 transforms to %28x%2B9%2F2%29%5E2-33%2F4. So x%5E2%2B9x%2B12=%28x%2B9%2F2%29%5E2-33%2F4.


So y=x%5E2%2B9x%2B12 is equivalent to y=%28x%2B9%2F2%29%5E2-33%2F4.