SOLUTION: How do you convert functions standard form to vertex form? Problem: y= x2-4x=6

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Question 170146This question is from textbook prentice hall mathematics California algebra 2
: How do you convert functions standard form to vertex form?
Problem: y= x2-4x=6 This question is from textbook prentice hall mathematics California algebra 2

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do you convert functions standard form to vertex form?
Problem: y= x^2-4x+6
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Complete the square with the x terms:
x^2-4x+4 = y-6+4
(x-2)^2 = y-2
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This shows you the vertex is at (2,2) and p= 1/4
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-4x%2B6 Start with the right side of the equation.


Take half of the x coefficient -4 to get -2. In other words, %281%2F2%29%28-4%29=-2.


Now square -2 to get 4. In other words, %28-2%29%5E2=%28-2%29%28-2%29=4


x%5E2-4x%2Bhighlight%284-4%29%2B6 Now add and subtract 4. Make sure to place this after the "x" term. Notice how 4-4=0. So the expression is not changed.


%28x%5E2-4x%2B4%29-4%2B6 Group the first three terms.


%28x-2%29%5E2-4%2B6 Factor x%5E2-4x%2B4 to get %28x-2%29%5E2.


%28x-2%29%5E2%2B2 Combine like terms.


So after completing the square, x%5E2-4x%2B6 transforms to %28x-2%29%5E2%2B2. So x%5E2-4x%2B6=%28x-2%29%5E2%2B2.


So y=x%5E2-4x%2B6 is equivalent to y=%28x-2%29%5E2%2B2.


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Answer:


So the equation y=x%5E2-4x%2B6 in vertex form is y=%28x-2%29%5E2%2B2