In the left Sketch you can control the shape and position of the parabola
y = a x2 + b x + c
by using the Controllers below the graph.
Parabola and the coefficient controllers
Zeros in the complex plane
Problems: How do the zeros change when you
change c and keep the others fixed as a = 1 and b = 0?
change b and keep the others fixed as a = 1 and c = -1?
change a and keep the others fixed as b = 0 and c = -1?
change b and keep the others fixed as a = 1 and c = 1?