# 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 in the
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.
More
Maths Calculators and Solvers .