Theory:

Let the graph of the parabola be \(y = ax^2 + bx + c\). The solutions of the quadratic equation are the \(x\) coordinates of intersection of the curve with \(X\) axis.
The steps to find the solution of the quadratic equation graphically is given by:
 
Step 1: Draw the graph of the equation \(y = ax^2 + bx + c\).
 
Step 2: (i) If the graph intersects the \(X\) - axis at only one point, then the given quadratic equation has only one root or two real and equal roots.
 
(ii) If the graph intersects the \(X\) - axis at two distinct points, then the given quadratic equation has two real and unequal roots.
 
(iii) If the graph does not intersect the \(X\) - axis at any point, then the given equation has no real root.