Parabola Formula

The parabola can be described as a U-shaped curve opening either upward or downward; more graphically, it is a curve that opens either upwards and downwards and left and right. We restrict ourselves to vertical parabolas, which allows for easier understanding: all points (x, y) are equidistant from a fixed point called the focus and a fixed line called the directrix.

Vertex is the coordinate from which the parabola takes its sharpest turn. It is the point at which the parabola intersects the axis and cannot go any higher or lower in a coordinate plane.

The curve is generated along with a straight line for the directrix. The parabola curves away from this line. The directrix is perpendicular to the axis of symmetry .

The Parabola Formula for the equation of a parabola given in its standard form, y = ax2 + bx + c is given below :

Solved Examples

Question: Find the vertex, focus and directrix of a parabola of equation y = 5x2 + 3x + 2.

 

Solution:

 

Given,

              y = 5x2 + 3x + 2

Comparing the above equation with the general form of parabola equation y = ax2 + bx + c we get,

               a = 5 

               b = 3 

               c = 2 

 

Vertex of a parabola  = 

=      ,

=      ,   

= ,

 

Focus of a parabola =

  =

 =      ()

 

   = ()

  =

   =

Directrix of a parabola

 

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