Here is the graph of y = x^2+bx ( leading coefficient is set to 1 initially ).Use the slider of b to find out how the graph changes with b. Where are the intercepts and vertex?
Now adjust the value of c from 0 to generate another graph y = x^2+bx+c. Can you put the second graph just about the x-axis? What kind of expression do you obtain when the graph touches the axis?