This environment differs from the previous one in an interesting way. In this environment you enter your equation f(x) = g(x) by fitting a quadratic function f(x) to three blue points that you can place anywhere on the screen, and a second quadratic function, g(x), by fitting it to three red points that you can place anywhere on the screen.
You can then, just as before, transform your original equation into the ‘solution equation’ form
by dragging the RED, BLUE and BLACK dots. The solution set of the equation can then be gotten by taking the square root of both sides yielding
The same challenge applies –
Dragging the BLACK dots changes both functions, but dragging the RED dot changes only the RED function and dragging the BLUE dot changes only the BLUE function.
This means that when you drag either the RED dot or the BLUE dot you are changing only one side of the equation!! Why is this legitimate? Why are we taught that you must do the same thing to both sides of the equation? What is true about all the legitimate things you can do to a quadratic equation?
What do the solution sets of quadratic inequalities look like?