# Parabola Calculator Given its Vertex and a Point

   

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.
The problem has no solution if $$h = x_0$$ or $$k = y_0$$

 Vertex at: $$(h,k)$$ = (1 , 3) Given Point at: $$(x_0,y_0)$$ = (5 , 0) Decimal Places = 3 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.
Maths Calculators and Solvers.