Parabola Equation

A parabola is a conical section formed by the intersection of a conical right circular surface and plane which is parallel to the straight line generated at that surface. The parabola can also be generated by examining the point called as focus and the line called as directrix. The locus of all points in the plane which are at equal distances from both the point and the line is said to be as the parabola. The line which passes through the focus (line which splits parabola in the middle) and lies perpendicular to the directrix is known as the “Axis of Symmetry”. Also the point present on this symmetry of axis which will intersect the parabola is known as the “Vertex”. In this vertex point, the curvature will be always greatest. A parabola can be opened up and down, left and right or even in some other arbitrary directions. They can be rescaled or repositioned in order to fit exactly with any other parabola, which implies that all parabolas are similar.

Standard form of a Parabola Equation
The general form for finding the Equation of a parabola is given as,
Y = ax2 + bx + c, where ‘x’ and ‘y’ are the points on the parabola.
In the above equation, when the value of ‘a’ is greater than zero, then the parabola will open upwards and when the value of ‘a’ is lesser than zero, then the parabola will open downwards. Also, the axis of symmetry will be the line of ‘x’ value equaling to negative of ‘b’ divided by 2a.

Parabola Equation Vertex
The point where the parabola will cross its axis is simply said as the vertex of a parabola equation. From the above standard equation of parabola, it implies that when the coefficient of x2 term occurs as positive, then the vertex will be at lowest point drawn on the graph. Similarly, when comes with negative coefficient of x2, it will be at highest point which can be said to be at the “U’ shape top.
The vertex form of a parabola equation can be written as,
Y = a(x-h) 2 + k, where ‘h’ and ‘k’ are the vertices of a parabola.

The parabola can also form into horizontal direction in the graph extending through the horizontal axis. The horizontal parabola Equation is simply as same as the standard form of parabola equation.

There are numerous websites which provide Parabola Equation solver in which when we give the vertex and focus of the parabola, it will automatically generate the standard and vertex form of the parabola.