Question 202264: Find the vertex of the quadratic function f(x) = -(x-2)^2+3. Does this function have a maximum or a minimum? How do you know?
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! Basic form for a parabola is ,,,,(y-k) = A ( x-h)^2,,,where (h,k( is vertex,,,,and sign of A indicates (upward if positive) or (downward if negative)
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y= -(x-2)^2 +3
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(y-3) = (-1) (x-2)^2,,,A=-1,,,k=3,,,h=2
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the vertex is at (2,3) pointing downward,,,,therefore this is a max
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to check, look at coordinates just before and after vertex
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if x=1.75, y=-.0625
if x= 2.25,,,y=-.0625
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since both are lower than (3), it is a max and parabola is pointed downward
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