SOLUTION: please help me solve this problem. y=x2+4x thats x squared. i need it written in vertex form.

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Question 166637: please help me solve this problem.
y=x2+4x
thats x squared.
i need it written in vertex form.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to write x%5E2%2B4x in vertex form, we need to complete the square for x%5E2%2B4x


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Completing the Square:


x%5E2%2B4x Start with the given expression.


Take half of the x coefficient 4 to get 2. In other words, %281%2F2%29%284%29=2.


Now square 2 to get 4. In other words, %282%29%5E2=%282%29%282%29=4


x%5E2%2B4x%2Bhighlight%284-4%29 Now add and subtract 4. Notice how 4-4=0. So the expression is not changed.


%28x%5E2%2B4x%2B4%29-4 Group the first three terms.


%28x%2B2%29%5E2-4 Factor x%5E2%2B4x%2B4 to get %28x%2B2%29%5E2.


So after completing the square, x%5E2%2B4x transforms to %28x%2B2%29%5E2-4. So x%5E2%2B4x=%28x%2B2%29%5E2-4.



So y=x%5E2%2B4x is equivalent to y=%28x%2B2%29%5E2-4.


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y=%28x%2B2%29%5E2-4 Start with the previous equation


y=%28x-%28-2%29%29%5E2-4 Rewrite x%2B2 as x-%28-2%29


y=1%28x-%28-2%29%29%5E2-4 Place a "1" outside the parenthesis.


Now y=1%28x-%28-2%29%29%5E2-4 is in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=-2 and k=-4