Solving Quadratic Equations by Factoring Students will be able to use factoring to solve quadratic equations.

Terminology A function is written f(x) = ax2 + bx + c. In functions, the x-intercepts (or the zeros) are the points where the graph crosses the x-axis. An equation is written y = ax2 + bx + c. In equations, the solutions (or the roots) are the points where the graph crosses the x-axis. FHS Quadratic Function

Solutions of Quadratic Equations To find the solutions of a quadratic equation, we want to find the x-coordinates of points where y = 0. Quadratic equations can have 2, 1 or 0 solutions. Let’s see how that can happen. This has 2 solutions: This has 1 solution: These have no solution: FHS Quadratic Function

Solutions of Quadratic Equations The Zero Product Property says that if the product of two quantities equals zero then at least one of those quantities must equal zero. Put the quadratic in the standard form: y = ax2 + bx + c. Replace y with a 0. Factor the equation: 0 = ax2 + bx + c Set each factor equal to 0 and solve for x. FHS Quadratic Function

Example (cont.) Find the exact solutions by factoring. If the first term is negative, change all of the signs in the equation. This will make the trinomial much easier to factor. Now we will factor this trinomial. Thus: or FHS Quadratic Function