If you can see the maximum or minimum point of the parabola, let that point be (x0,y0). Then the equation will be of the form
y = m(x-x0)^2+y0
Then use another point to find m. If the parabola is open upwards (like a smile), m will be positive; if the parabola is open downwards (like a frown), m will be negative.
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Worry is a misuse of imagination.
Fantasizing about Guru champion BlAcK TuRtLe, however, is a great use of it.