SOLUTION: Find the exact vertex of the parabola algebraically... f(x) = -3x^2 + 5x + 1

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Question 192072: Find the exact vertex of the parabola algebraically...
f(x) = -3x^2 + 5x + 1
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = -3x^2 + 5x + 1
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Use completing the square:
3x^2 -5x + ? = -y + 1 + ?
3(x^2 - (5/3)x + (5/6)^2) = -y + 1 +3(5/6)^2
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3(x-(5/3))^2 = -y + 1 + (25/12)
3(x-(5/3))^2 = -y + (37/12)
3(x-(5/3))^2 = -(y - (37/12)
(x-(5/3))^2 = (-1/3)(y-(37/12))
Vertex: (5/3 , 37/12)
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Graph:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C-3x%5E2%2B5x%2B1%29
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Cheers,
Stan H.