You can make a quadratic function by dragging the three RED points almost anywhere on the screen (why almost?). The function will have the form
quadratic(x) = ,
where U and V are real numbers and the value of C is a real number.
Now try to build the same quadratic function by combining the appropriate amounts of quadratic term, linear term and constant term using the BLUE sliders.
Try to do this without displaying the functional form of the RED quadratic function you have made.
You can check your work by showing the expressions for the functions on the screen.
CHALLENGE - A student asks "How do you know that you can always make a quadratic function given three points?" What do you respond?
Can three points define any other kind of function? How many RED dots would you need to make a cubic function? How do you know?
A student asks “Is there a way to think about slope for a quadratic function?” What do you respond?
What questions could/would you pose to your students based on this applet ?