SOLUTION: How would you change x^2-6x+5 to vertex form

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Question 183458: How would you change x^2-6x+5 to vertex form
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
In order to get x%5E2-6x%2B5 into vertex form, we need to complete the square:


x%5E2-6x%2B5 Start with the given expression.


Take half of the x 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


x%5E2-6x%2Bhighlight%289-9%29%2B5 Now add and subtract 9. Make sure to place this after the "x" term. Notice how 9-9=0. So the expression is not changed.


%28x%5E2-6x%2B9%29-9%2B5 Group the first three terms.


%28x-3%29%5E2-9%2B5 Factor x%5E2-6x%2B9 to get %28x-3%29%5E2.


%28x-3%29%5E2-4 Combine like terms.


So after completing the square, x%5E2-6x%2B5 transforms to %28x-3%29%5E2-4.


Now the expression %28x-3%29%5E2-4 is in vertex form.