SOLUTION: Please help me with making 1/2y^2-3y+13/2 into standard form

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Question 196648: Please help me with making 1/2y^2-3y+13/2 into standard form
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to complete the square.




%281%2F2%29y%5E2-3y%2B13%2F2 Start with the given expression.


%281%2F2%29%28y%5E2-6y%2B13%29 Factor out the y%5E2 coefficient 1%2F2. This step is very important: the y%5E2 coefficient must be equal to 1.


Take half of the y coefficient -6 to get -3. In other words, %281%2F2%29%28-6%29=-3.


Now square -3 to get 9. In other words, %28-3%29%5E2=%28-3%29%28-3%29=9


%281%2F2%29%28y%5E2-6y%2Bhighlight%289-9%29%2B13%29 Now add and subtract 9 inside the parenthesis. Make sure to place this after the "y" term. Notice how 9-9=0. So the expression is not changed.


%281%2F2%29%28%28y%5E2-6y%2B9%29-9%2B13%29 Group the first three terms.


%281%2F2%29%28%28y-3%29%5E2-9%2B13%29 Factor y%5E2-6y%2B9 to get %28y-3%29%5E2.


%281%2F2%29%28%28y-3%29%5E2%2B4%29 Combine like terms.


%281%2F2%29%28y-3%29%5E2%2B%281%2F2%29%284%29 Distribute.


%281%2F2%29%28y-3%29%5E2%2B2 Multiply.


So after completing the square, 1%2F2y%5E2-3y%2B13%2F2 transforms to %281%2F2%29%28y-3%29%5E2%2B2.


In other words, %281%2F2%29y%5E2-3y%2B13%2F2=%281%2F2%29%28y-3%29%5E2%2B2.