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High School — Mathematics
Patterns, Relations and Algebra


Core Resources

    Patterns, Functions, and Algebra


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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.


      Solve by completing the square.


      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:




      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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