SOLUTION: Can you help me write this in standard form? y=x^2+2x+2

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Question 452786: Can you help me write this in standard form?
y=x^2+2x+2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To write y=x%5E2%2B2x%2B2 in standard form, we must complete the square for x%5E2%2B2x%2B2


x%5E2%2B2x%2B2 Start with the given expression.


Take half of the x coefficient 2 to get 1. In other words, %281%2F2%29%282%29=1.


Now square 1 to get 1. In other words, %281%29%5E2=%281%29%281%29=1


x%5E2%2B2x%2Bhighlight%281-1%29%2B2 Now add and subtract 1. Make sure to place this after the "x" term. Notice how 1-1=0. So the expression is not changed.


%28x%5E2%2B2x%2B1%29-1%2B2 Group the first three terms.


%28x%2B1%29%5E2-1%2B2 Factor x%5E2%2B2x%2B1 to get %28x%2B1%29%5E2.


%28x%2B1%29%5E2%2B1 Combine like terms.


So after completing the square, x%5E2%2B2x%2B2 transforms to %28x%2B1%29%5E2%2B1. So x%5E2%2B2x%2B2=%28x%2B1%29%5E2%2B1.


So y=x%5E2%2B2x%2B2 is equivalent to y=%28x%2B1%29%5E2%2B1.


which is now in standard form.