This calculator finds the equation of parabola with vertical axis given its vertex of the parabola and a point on the parabola.

Solve the above equation to find coefficient \( a \) \[ a = \dfrac{y_0 - k}{(x_0 - h)^2} \]

Note that

1) if \( h = x_0 \), the denominator in \( a \) is equal to zero and the problem has no solution because both the vertex and the given point \( A \) are in the same vertical line.

2) if \( k = y_0 \), there is no parabola because both the vertex and the given \( A \) are in the same horizontal line.

Three equations are displayed: in vertex form as given above, an exact one (middle one) where the coefficients are in fractional forms a third equation with approximated (if necessary) coefficients in decimal form.

You may also change the number of decimal places.

The problem has no solution if \( h = x_0 \) or \( k = y_0 \)

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