Quadratics in Factored Form

When studying quadratics in algebra, students spend a fair amount of time learning to factor them. But why is a factored quadratic useful? The Quadratics in Factored Form Gizmo can help students answer that question.

The Gizmo presents a quadratic in its factored form, with linear factors (x – r1) and (x – r2). As students vary r1 and r2, they will see that the values are the x-coordinates of the x-intercepts and make the function equal to zero.

You can take the investigation further, if you like. Does the shape of the graph change as you vary r1 and r2? How does the leading coefficient (a) affect the graph? Does a change the x-intercepts? Why or why not? What does the graph look like when both roots are the same? Students can expand their study to include quadratics with no real roots in the Quadratics in Polynomial Form and the Roots of a Quadratic Gizmos.