Jadhav Quadratic Formula, evaluates accurate values of numbers lying on x-axis of the co-ordinate plane corresponding to the respective y-axis points. Derived by Indian-Mathematical Scholar

## Formula

If we are given the points of y-axis with the quadratic equation it followed then we can find the respective x-axis points by: $x = {-b \pm \surd b^2 - 4a (c-y)}/2a$

## Requirements

For this formula to function we should have the quadratic equation along with given y-axis point and can get the 2 corresponding points on the x-axis.

## Nomenclature

• b: Coefficient of $x$.
• a: Coefficient of $x^2$.
• c: Constant term of equation.
• y: The given y-axis point.

## Derivation

Let the quadratic equation be : $ax^2+bx+c$

Now at some given value of x the function of graph will give the value for point lying on y-axis

So, we can equate $ax^2+bx+c=y$ $x^2+bx/a+c/a = y/a$ (dividing all terms by a) ${x^{2}+2bx/2a+b^2/4a^2+c/a=y/a+b^2/4a^2}$ (adding ${b^2/4a^2}$ on both sides) $[{x+b/2a}]^{2}+c/a=y/a+b^{2}/4a^{2}$ $[{x+b/2a}]^{2}=y/a+b^{2}/4a^{2}-c/a$ $x+b/2a=\pm\surd[y/a+b^{2}/4a^{2}-c/a]$ $x+b/2a=\pm\surd[4ay+b^{2}-4ac]/\surd\left\vert 4a^2 \right\vert$ $x=-b/2a\pm\surd[4ay+b^{2}-4ac]/\surd\left\vert 4a^2 \right\vert$ $x=[-b\pm\surd b^{2}-4a(c-y)]/2a$