MANY PARABOLAS

The applet shows the graph of y = a(x + 1)(x – 3).
Note: If the applet becomes distorted, click "init" to reset. To clear traces. click "clear".

Click on the slider to vary the value of parameter a. What happens? What does it mean?

Click the slider to solve the following problems visually. How can you be sure you are correct? Prove that you are correct!
For what value(s) of a does the graph of y = a(x + 1)(x – 3):

pass exactly through the point A(3, -7)?    a =     
pass exactly through the point B(6, -7)?    a =     
have a minimum value of -5?    a =