SOLUTION: Determine the vertex of y=xsquared-8x+22.

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Question 90248: Determine the vertex of y=xsquared-8x+22.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First determine the x-value:
x=-b%2F%282a%29

x=--8%2F%282%2A1%29 Plug in b=-8 and a=1

x=4 Simplify


Lets evaluate f%284%29

f%28x%29=x%5E2-8x%2B22 Start with the given polynomial


f%284%29=%284%29%5E2-8%284%29%2B22 Plug in x=4


f%284%29=%2816%29-8%284%29%2B22 Raise 4 to the second power to get 16


f%284%29=%2816%29-32%2B22 Multiply 8 by 4 to get 32


f%284%29=6 Now combine like terms


So the vertex is (4,6)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the vertex of y=x^2-8x+22.
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Complete the square on the x-terms and keep the equation balanced:
y = x^2-8x+(8/2)^2 +22 - (8/2)^2
y = (x-4)^2 + 88/4 - 64/4
y = (x-4)^ + 6
y-6 = (x-4)^2
Vertex at x=4,y=6
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graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-8x%2B22%29
Cheers,
Stan H.