Parabola is a special curve that has a shape similar to an arch. It is one of the kinds of conic sections and this symmetrical plane curve is the outcome of the intersection of a right circular cone with a plane surface. It comes out in U-shape and displays some very unique and particular properties. Whenever we take any point on this curve it will be on equal distance from the fixed point which we call focus or a straight fixed line which we call parabola directrix. However, Calculations that involve parabola can be simplified using a parabola calculator.
We can represent it in a standard format with the help of a parabola equation. There are four forms to represent the parabola formula
- The simplest form can be represented as y=x2
- General form can be represented as y2=4ax
- Standard form of parabola equation is: x=ay2+by+c
- Parabola equation in the vertex form can be represented as: x=a(y-k)2+h
On the other hand, with the help of a parabola calculator, it becomes easy to make calculations where you need to use its equations.
How to find the equation of a parabola in a vertex form?
It is possible to determine the equation of the parabola in a vertex form with the help of manual calculations but, for a quick and error-free solution, it will be wise to use a parabola calculator online. One of the most efficient tools for the quick calculation of parabola in a vertex form is discussed below:
This Parabola equation calculator gives us parabola in a vertex form quickly and accurately within no time. You just have to follow some simple steps:
- This calculator gives you the option to select the parabola equation from its drop-down menu. You can either select the equation in the standard format or vertex format.
- After selecting the equation format it will display it instantly. You can add your values in the given fields.
- On Clicking the calculate button you will get the equation of the parabola in a vertex format as an output within a few seconds.
- It also displays all the parameters of the parabola such as its Vertex, Focus, Eccentricity, Directrix, Latus rectum, Axis of symmetry, x-intercept, y-intercept.
- This parabola calculator also gives you a graphical representation of the parabola in the end.
Why Is the Vertex Form of the Parabola equation being Useful?
The vertex form of the parabola equation serves as an alternative way to writing out the equation of a parabola. Usually, we write the quadratic equation as ax2+bx+c. Which can represent the parabola when we make a graph out of it. From this format, it becomes easy to find the roots of the equation by setting the equation equal to zero. It is the point where the parabola hits the x-axis. At this point, we can also use the quadratic formula. However, for the calculation of the vertex of a parabola, the standard quadratic form is not very helpful. As an alternative, it becomes mandatory to convert the quadratic equation into vertex format. In both formats from the above formulas, y is the y-coordinate, x is the x-coordinate, and a is the constant that explains whether the parabola is facing up (+a) or down (−a). The basic difference between a parabola’s standard form and vertex format is that the vertex form gives you the parabola’s vertex: (h,k). However, a parabola calculator is the best option to deal with these two simultaneously.