Any time you need to solve an equation that involves both x and the square of x, it is usually necessary to move everything to one side and find the roots (or solutions) of a quadratic equation in the form ax2 + bx + c = 0. While many quadratic equations can be solved by factoring, often the best way to find the answer is to use the quadratic formula.
The Roots of a Quadratic Gizmo is a great introduction to solving quadratics because it demonstrates that the solutions of a quadratic equation are equal to the x-intercepts of the parabola of the corresponding quadratic function. Students can use the Gizmo to find the axis of symmetry, calculate the discriminant to find the number of real roots, and practice using the quadratic formula to find both real and complex roots for quadratic equations. Be sure to go through the derivation of the quadratic formula with your class, which is found in the Teacher Guide for this Gizmo.