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Completing the Square: Algebraic Approach to Quadratic Equations

This task focuses on using geometric and algebraic methods to complete the square for expressions of the form x^2 + bx, equations in the forms x^2 + bx = c, x^2 + bx + c = 0, and ax^2 + bx + c = 0. Students will employ geometric tiles to visualize the process and then solve algebraically. Completing the square offers an alternative method for solving quadratic equations when factoring is not straightforward. This post-assessment activity in Algebra I Unit 10-5 prepares students for Test Prep questions 45-49 on page 584.

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Completing the Square: Algebraic Approach to Quadratic Equations

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  1. Objective 10-5: Completing the Square • TASK: • Students will take geometric tiles for expressions of the form x2 + bxand add enough unit tiles to complete the square. • Students will complete the squarealgebraically for expressions of the form x2+ bx • Students will complete the square algebraically for equations of the form x2+ bx = c • Students will complete the square algebraically for equations of the form x2+ bx + c = 0 • Students will complete the square algebraically for equations of the form ax2+ bx + c = 0 • WHY: • Completing the square is used as another way to solve quadratic equations particularly for those when answering by factoring is not apparent.

  2. Algebra I Unit 10-5 Post Assessment • Test Prep page 584, #45-49.

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