SOLUTION: Determine the maximum or minimum value of the quadratic function. f(x)=x^2-6x+2

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Question 123806: Determine the maximum or minimum value of the quadratic function.
f(x)=x^2-6x+2

Found 2 solutions by stanbon, rapaljer:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the maximum or minimum value of the quadratic function.
f(x)=x^2-6x+2
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max or min occurs at x = -b/2a = 6/2 = 3
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f(3) = 3^2-6*3+2 = -7
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minimum at (3,-7)
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-6x%2B2%29
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Cheers,
Stan H.

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
You can do this algebraically or graphically. What is your choice? I think the easiest way is graphical.

graph%28300%2C300%2C-6%2C6%2C-10%2C10%2C+x%5E2-6x%2B2%29+
It looks like the minimum value of f(x) is y=-7.

Try algebraically to confirm this answer:
y=x^2-6x+2

There are several ways, probably the easiest of which is to find x=-b%2F%282a%29+, where a is the coefficient of x^2 and b is the coefficient of x. Therefore, a=1, b=-6, so x=-b%2F%282a%29+=6%2F2=3

y=x%5E2-6x%2B2, where x=3
y=3%5E2-6%2A3%2B2
y=9-18%2B2
y=-7 is the minimum value

R^2