Understand quadratic equation and it's solution using graph

Author:
Mathguru
Topic:
Equations
If we change the values of a, b and c using their respective slide bars we will see that position of the graph (parabola) gets changed. Here a, b and c are coefficients of the quadratic function y=ax^2+bx+c, and roots of the equation ax^2+bx+c=0 are α, β= (-b±(b^2-4ac)^(1/2))/2a
Questions to think about. What is the difference in shapes of the graph when a>0 and a<0? What is the difference in the shapes of the graph when b^2>4ac and b^2<4ac. Set the value of a, b and c such that b^2=4ac , what do you observe. For example set a=1, c=1 and b=2