Modify quadratic equations and observe the properties of their roots.
[i]Answer these open ended questions on your own or with others to form deeper math connections.[/i]
What do you notice about the roots of the equation? Where on the graph do the roots of the equation lie?
What does the graph of a quadratic equation with exactly one root look like? Where does the [math]x[/math]-intercept lie?
What do you notice about the graph of a quadratic equation with no real roots?
What does the graph of [math]f(x)[/math] look like when the coefficient for [math]x^2[/math] is 0?
What are we finding by setting [math]f(x)[/math] equal to 0?