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Parabola Equation Calculator For You To Use

What is a parabola? It is a U-shaped symmetrical curve with every point lying on it being equidistant from both a certain point.

Therefore, we can use a parabola calculator to calculate the path made by an object in projectile motion.


The parabola equation calculator displays the graph of the parabola after entering the required values. Our parabola generator makes the calculation faster and displays the parabola graph in a fraction of seconds.


It can serve as the following:

  • Latus rectum calculator
  • Focus and directrix calculator
  • Parabola standard form calculator
  • Focal parameter calculator
  • Axis of symmetry and eccentricity calculator.

The parabola equation finder will help you solve your engineering algebraic problems and academic equations easily.

How To Find the Equation of a Parabola

Use the formula to find the equation of a parabola calculator in vertex form:

Now, the standard form of a quadratic equation is y = ax² + bx + c

Therefore, the equation of a parabola calculator in its vertex form is y = a(x-h)² + k, where:

  • a is similar to the a coefficient in the standard form;
  • h is the parabola vertex x-coordinate
  • k is the parabola vertex y-coordinate

To find the values of h and k, use the equations below:

h = - b/ (2a)

k = c - b²/ (4a)

On the other hand, the formula of the parabola standard form calculator is:

y = (x2 / (4a)) - (hx / 2a) + (k + (h2 / (4a)))


h = is the x-coordinate of parabola Vertex

k = is the y-coordinate of parabola Vertex

x = is the x-coordinate of parabola Focus

y = is the y-coordinate of parabola Focus

Here is an example: 

#1: Find the directrix of the parabola. (using either the parabola calculator or the equation)

y = c - (b² + 1)/ (4a) = -4 - (9+1)/8 = -5.25

#2: Calculate the coordinates of the vertex, where a = 2, b = 3 and c = -4.

h = - b/ (2a) = -3/4 = -0.75

k = c - b²/ (4a) = -4 - 9/8 = -5.125

Steps To Using the Parabola Equation Solver

The procedure is as simple as shown below: 

  1. Enter the necessary data in the input field
  2. Hit the button “Submit”
  3. The parabola graph will finally be displayed in the new window

You do not need any rocket science knowledge to use this parabola solver effectively. Provided you are armed with the formula; you can easily use the parabola equation calculator from points. On top of that, the parabola generator has a user-friendly site that can be used by amateurs and pros.

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