Parabola Calculator Given its Vertex and a Point

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

Formulas Used in the Calculator

The equation of a parabola whose vertex is given by its coordinates \( (h,k) \) is written as follows \[ y = a(x - h)^2 + k \] For the point with coordinates \( A = (x_0 , y_0) \) to be on the parabola, the equation \( y_0 = a(x_0 - h)^2 + k \) must be satified.
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.

How to Use the Calculator

1 - Enter the \( h \) and \( k\) coordinates the vertex and the coordinates \( x_0 \) and \( y_0 \) of the point on the parabola and press "Calculate".
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 in the
The problem has no solution if \( h = x_0 \) or \( k = y_0 \)

Vertex at: \( (h,k) \) = ( , )

Given Point at: \( (x_0,y_0) \) = ( , )
Decimal Places =
Vertex Form     $y=$
General Form with Fractional Coefficients     $y=$
General Form with Decimal Coefficients $y=$



More References and Links to Parabola

Three Points Parabola Calculator.
Three Points Circle Calculator.
Points of Intersection of Two Circles - Calculator.
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Maths Calculators and Solvers .

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