Lesson 10: 9-4 Solving Quadratics by Factoring

1. What technique is used to factor the expression on the left side of the equation?
2. Why are there two solutions?
3. When will the quadratic equation have one solution?

Square root Property
Zero product property

A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.
A.REI.4b Solve Quadratic equations by inspection (e.g. for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a+bi, a-bi for real numbers a and b

SAT questions related to solving quadratics: 2-3-13,3-3-14,1-3-16,5-3-3,8-3-16,1-4-25; analyzing graphs: 3-4-12,8-3-11,8-4-19,6-3-11

Quadratic equations can be solved using several different methods. Factoring can be a quick method. Once a polynomial has been factored, the Zero Product Property may be used to find the roots of the equation. If the polynomial is difficult to factor or is not factorable, then other methods must be used.

Froghoppers are insects commonly found in Africa, Europe and North America. They are only about 6 millimeters long, but they can jump up to 70 times their body height. A froghopper's jump can be modeled by the equation h = 12t-16t^2, where t is the time in seconds and h is the height in feet. You can use factoring and the Zero product property to determine when the froghopper will complete its jump.

Some students may suggest solving a quadratic equation by dividing by the variable on both sides. This cannot be done because the value of the variable could be zero, and division by zero is undefined.

Provide each student with a sheet of grid paper. Have students begin by drawing a coordinate grid with two points on the x-axis plotted as the roots of a quadratic equation. Ask students to draw several parabolas that might be the graphs of different equations having those two points as their solutions. Point out that this demonstrates that the steps shown yield just one of the possible equations having the given roots.

Practice: Exercises 1 - 16

Exercises 50-61

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