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- Thread starter Neha Sanghvi
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Galileo

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[tex]a\left(x+\frac{b}{2a}\right)^2+\left(c-\frac{b^2}{4a}\right)[/tex]

You can see that it is equal to the graph of [itex]ax^2[/itex], but shifted vertically by [itex]c-\frac{b^2}{4a}[/itex] and horizontally by [itex]\frac{b}{2a}[/itex]. The a can be seen as a scaling factor in the y-direction. If it's positive, you have a 'dale-parabola', if it's negative it's a 'hill-parabola'.

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