Solve quadratic equations by factoring
The think-pair-share activity presents students with representations of all three types of trinomial factoring. Students are able to recognize that the property applies not only to monomials, but also to binomials, and is applicable for all real numbers. In applying it to binomial factors, they can use the property as a tool in a way that has not previously been represented. The Zero Product Property is an elementary concept that is familiar to students. By illustrating these connections, students can see how general solutions are possible. The example of x² + x - 6 shows students the relationship between the zeros of the function, the roots of the equation, and the constant terms of the binomial factors of the trinomial.
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The lesson includes recognizing and using trinomials in various forms. This lesson helps students to develop skills in solving quadratic equations by factoring and provides them with useful techniques for factoring and for understanding the rationale that supports finding solutions.
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Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
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Families of functions exhibit properties and behaviors that can be recognized across representations.