Parabola Calculator- parabola equation, meaning, formula

Parabola Calculator is a free tool available online that displays the graph for a given parabola equation. An online parabola calculator makes the calculation faster with accurate results within a few seconds. On the contrary, the basic parabola calculators will only allow you to input a parabolic equation in a standard form. Hence, it will display the x and y coordinates of the vertex focus and directrix. Some basic calculators will also provide you with the parabola equation in vertex form.

Parabola calculator version 2.0

There are various websites that actually provide you with this free calculator.  Parabola calculator version 2.0 is a popular app written to help the user design solar collectors or wifi projects.  In addition to this, there are also other various websites providing free calculators.

Furthermore, these calculators save your time and increase your efficiency. Advanced parabola calculators will also display the graph with good graphics that significantly save your time. These calculators increase the scope of visually learning. Meanwhile, users can explore various forms of graphs just by entering the equation. Students tend to relate the application of these complex shapes in an easier manner. Students and Researchers, especially people working in advanced math fields where the applicability of these calculators is pretty high, find it more convenient to use than struggling with calculations.                      


 Parabola Calculator with vertex and focus and how to solve them

  • The parabola calculator is used to solve quadratic equations in both standard form and vertex form. First, you will need to calculate the parabola vertex, focus, and directrix by giving the inputs. The calculator can find results for you in two ways. First, on the equation of the parabola from the given variables or if the question provides you with the axis of symmetry.
  • It is easier to use and convenient at the same time. you get these calculators free of cost on the internet. First, you need to enter the three coordinates chosen for your axis .Click on the submit option. And you get an accurate answer. Henceforth the graph will be displayed in a new window. There are also calculators which can display the result just by entering the parabolic equation. Parabola calculators fall under the category of advanced calculators.
  • Complex questions always require the calculator’s help. .. As a result, depending on the type of problem you are solving, choose your ideal calculator. So set your objective beforehand.
  • To get maximum benefits choose the advanced level calculators therefore it will give you wider options. People tend to ignore them thinking it’s more complex but that’s not the case in most cases.

Parabola Calculator download

If you do not have a stable internet connection, you can download a parabola calculator in your laptop. You just have to type “parabola calculator download” in Google or any other search engine that you use. Subsequently, you find a number of calculator downloading websites popping up. You can use any of the available free websites to download the application.

Read Also:Derivative Of sin2x: Proof, Calculation, Chain Rule and Examples

Click on a website as per your choice. and you will have a download option to download the parabola calculator.

How to choose your ideal parabola calculator ?

First, Identify your question type.  Second, look for the required calculator. Third, decide if this calculator can fulfill your requirements. There is no strict rule to follow while choosing your ideal calculator. As long as the calculators are working you can go for the basic range of calculators. Notwithstanding the fact, advanced level calculators are more reliable and give you better results with an intensified display.

Before we discuss more on  Parabola Calculator.

First, we need to  clear our ideas about parabola and its equations which are equally important

What is a Parabola?

Parabolas are graphs of quadratic functions.

 is a basic quadratic function while  a,b,c are real numbers and

Parabola is a plane curve-like structure that is mirror-symmetrical and looks like a U. In addition to this there is one more opinion on the shape of a parabola. It is cone-shaped created from the intersection of a right circular conical surface and a plane running parallel to another plane which is tangent  to the conical surface. A parabola is created when the angle between the plane and the axis is equal to the vertex angle in a conic section. Moreover In terms of mathematics, the parabola has a fixed point known as focus and a fixed line known as directrix. The locus( path ) of points on a plane that is equidistant  from the focus and the directrix is defined as a Parabola

Equally important point to remember is that a focus does not lie on the directrix. In simple terms, we can define a parabola as an accumulation of all points in a plane. The plane lays at an equidistant from a stationary line ( directrix) and a stationary point (focus) represented as F.

A parabola looks like this.


Parabola key terms

Focus:  Singular focus, foci, or focuses. These are the points. the focus of the parabola lies on the axis

Directrix: a directrix is a fixed-line used to describe a conic section. In parabolas, there is one directrix

Latus Rectum: latus rectum is derived from the Latin term latus which means sides and rectum which means straight. A straight line running parallel to the directrix of the conic section and passing through its focus is known as the latus rectum. The general representation of a latus rectum is 4a

When we draw a parabola on a graph the maximum value or the minimum value we get on the parabola is known as a vertex of the parabola.

Standard Equation of parabola used in parabola calculator

  • The standard equation of a regular parabola is as long as the directrix is parallel to the y-axis.
  • If the directrix is parallel to the x-axis the standard equation changes to .
  • Furthermore , if the parabola is in the negative quadrant and the directrix is  parallel to the y-axis then the standard equation is
  • Moreover, if the parabola is in the negative quadrant while directrix is parallel to the x-axis then the standard equation is


The general equation of a parabola in parabola calculator

where () denotes the vertex.

The parabola equation in its vertex form is

 where a is the standard form of coefficient a.

  h and k denotes the x and y coordinates respectively.

Formulas to calculate h an k are:


Parabola uses in real life

Parabola has got some amazing practical life uses:

  • Satellites ( in form of satellite dishes)
  • Radar ( in form of radar dishes)
  • Moreover a ball is thrown into the air also follows  a parabolic path
  • The tracks of a roller coaster with a rise and fall shows a parabola
  • fountains
  • flashlights                       


Parabola Formula helps in showing the general form of the parabolic path in the plane.  To get the the variables the formula given below is used

Point to remember   the direction of the parabola is determined by the value of

Vertex =  where

Latus  Rectum=

focus=(and Directrix =


First you need to find out the coordinates that you will plot on the graph.

Example 1:  , if you are to solve this

First, Determine the y-intercept. To do this, set x = 0 and solve for y.


 , 3

The y-intercept is (0, 3).

Second, Determine the x-intercepts. To do this, set y = 0 and solve for x.



 Third,Determine the vertex. One way to do this is to use the equation for the line of symmetry,


 to find the x-value of the vertex. In this example, a = −1 and b = −2:

Then,Substitute −1 into the original equation to find the corresponding y-value. We get 4 . The vertex is (-1,4).

Therefore, calculate extra points so that we have at least five points to plot. In this example, one other point will suffice. Choose x = −2 and find the corresponding y-value. We get the value as 3.Our fifth point is (-2,3). After getting the points altogether we can now plot them The graphic is shown below


The parabola tends to open in the downward direction.To summarize,  If the leading coefficient is negative then the parabola opens downward.The axis of symmetry is along the x-axis when the parabola opens to right.. if the coefficient of x is positive and is in the left when the coefficient of x is negative henceforth in the y-axis , when the axis of symmetry is along the y-axis the parabola tends to open upwards if the coefficient of y is positive and downwards if the coefficient of y is negative .

Parabola Graph Calculator

Just like parabola calculator, there are calculators that can find the graph of any quadratic equation. That too in parabolic shape. You can find them online, but can also download them on your pc or laptop.

Parabola equation with solved examples

This problem is to give you  more clarity  on sums of parabolic equation , Suppose the question asks you to find the length of  latus rectum, focus and vertex for a given equation .Example 2:  The equation of a  parabola is Find the length of the latus rectum ,focus and vertex.

solution:Given: Equation of a parabola: y2 = 24x,Therefore, 4a = 24,a = 24/4 = 6

Now, parabola formula for latus rectum is:

Length of latus rectum = 4a

= 4(6) = 24

Now, focus= (a,0) = (6,0)

Now, Vertex = (0,0)

The length of the latus rectum is 24, the focus is (6,0) and the vertex is (0,0).


Find the coordinates of the focus ,axis and latus rectum of the equation. .On comparing this question with our general equation we get the value of a =2

So the focus of the parabola is (2,0). and the equation of the directrix of the parabola is

x=-2. The length of the latus rectum is 4a  that is 4*2=8

Example 4:Given ,

Comparing with the standard equation we get , y^2= 4ax , we get 4a=¼  , a= 1( 4*4) =1/16 so the vertex is (0, 0) and the focus is =(0, -⅙). The equation of the axis is x= 0 and  the directrix is y= (1/16) . The length of the latus rectum is 4a= ¼

Final view on Parabola  Calculator

In Conclusion, Parabolic shapes have started gaining a lot of importance after their application has been popularized.  Further with the advent of science and technology various complex math have evolved in the process.Subsequently, there is an increase in demand for these calculators which saves our time. It’s equally important to do calculations manually, therefore, do not depend entirely on the calculators.



An online and easy tool that calculates the equation of a parabola as per the users’ requirement.


A parabola is a U-shaped symmetrical shaped curve on which the points are equidistant from the directrix and focus


The vertex of a parabola is the point at the line of intersection of the parabola and its line of symmetry.


y=a(x-h)^2+k or x=(y-k)^2+h . h and k represents the vertex.


Parabola is U-shaped


No, the focus is the fixed point whereas directrix is the fixed line.

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