Educator

Solving Equations by Graphing

• A quadratic equation is one that can be written in the form ax² + bx + c = 0, where a ≠ 0. Its solutions are called the roots of the equation.

• The roots of a quadratic equation are x-intercepts of the graph of the related quadratic function.

• A quadratic equation has 2 real roots if its graph has two x-intercepts, 1 real root if it has one x-intercept (in this case, the graph is tangent to the x axis and the root is called a double root), and no real roots if it has no x-intercepts.

• If a root is not an integer, estimate the root by stating the two consecutive integers it lies between.

• In general, use graphing to solve an equation only if you would be satisfied with an estimate for the solutions, not exact values.

• A real number is a zero of the quadratic function f(x) if and only if it is a root of the equation f(x) = 0.