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High School — Mathematics
Patterns, Relations and Algebra

Overview

Core Resources

    Patterns, Functions, and Algebra

    Strategies

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      Online Resources

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      Strategies: Advanced Work

      The following activities are suggestions for working with students who are ready for advanced work. We hope that the activities spark ideas and conversations among teachers about useful classroom strategies that can supplement existing curriculum.

      Solving Quadratic Equations by Completing the Square

      Completing the square requires students to factor and multiply polynomials.


      Problem

      Solve by completing the square.

      Method

      First, we first move the constant term to the right hand side of the equation:

      .

      We want the left side of the equation to be a trinomial that factors easily, so we take half of the x-term's coefficient (6) and square the result:

      .

      We add the result, 9, to both sides of the equation:

      .

      Now the left-hand side can be factored into . Our equation is now:

      .

      Next, we take the square root of both sides to get:

      .

      Finally, we solve for x. In this case we subtract 3 from both 4 and -4 to get:

      .

      Answer

      Extension

      Once students have a lot of practice completing the square, ask them to complete the square for the general quadratic equation: . If done correctly, the result is the quadratic formula!

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