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Quadratic Equations: Methods for Solving and Applications

This PowerPoint presentation provides a comprehensive review of solving quadratic equations using different methods such as factoring, the square root property, completing the square, and the quadratic formula. It also includes examples and applications of these methods.

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Quadratic Equations: Methods for Solving and Applications

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  1. Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

  2. Quadratic Equations Chapter 11

  3. 11 Quadratic Equations 11.1 Review of Solving Equation by Factoring 11.2 The Square Root Property and Completing the Square 11.3 The Quadratic Formula Putting It All Together 11.4 Equations in Quadratic Form 11.5 Formulas and Applications

  4. 11.1 Review of Solving Equations by Factoring In section 7.5, we learned how to solve quadratic equations by factoring. We will Not be able to solve all quadratic equations by factoring, however. Therefore, we Need to learn other methods. In this chapter, we will discuss the following four Methods for solving quadratic • Four Methods for Solving Quadratic Equations • Factoring • Square root property • Completing the square • Quadratic formula 1. Review How to Solve a Quadratic Equation by Factoring

  5. Example 1 Solve by factoring. Solution Step 1: Write equation in standard form . Subtract 10 on both sides. Simplify. Step 2: Factor expression. Factor. Set each factor equal to 0. Solve. or

  6. Example 2 Solve by factoring. Solution Step 1: Write equation in standard form . One side of the equation must equal zero in order to use the zero product rule. Multiply both factors. Gather like terms on one side of equation. Step 2: Factor expression. Factor. Set each factor equal to 0. Solve. or The solution set is { -1, 8}.

  7. Example 3 Solve by factoring. Solution Although this is a cubic equation and not quadratic, we can solve it by factoring. Get zero on one side of the equal sign. Factor out x. Factor Set each factor equal to zero. Solve. The check is left to the student. The solution set is

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