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9.1 Completing the Square and the Quadratic Formula

9.1 Completing the Square and the Quadratic Formula. 1. 2. . Solve. Often times we are not able to a quadratic equation in order to solve it. When this is the case, we have two other methods: completing the square and the quadratic formula.

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9.1 Completing the Square and the Quadratic Formula

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  1. 9.1 Completing the Square and the Quadratic Formula

  2. 1. 2. Solve.

  3. Often times we are not able to a quadratic equation in order to solve it. When this is the case, we have two other methods: completing the square and the quadratic formula. • By learning how to the we can force a quadratic expression to factor. factor complete square

  4. Steps for Solving a Quadratic by Completing the Square • 1. Add or subtract the constant term to the other side (if necessary). • 2. Check to make sure the coefficient of is . If not, factor out the coefficient of and divide both sides of the equation by this number. • 3. Take of b, square it, and add it to sides. • 4. Make the left side a square of a binomial (example: ). • 5. Simplify the right side. • 6. Take the square root of each side. (make sure to use ). • 7. Solve for x. 1 half both ±

  5. 3. Solve by Completing the Square

  6. 4. Solve by Completing the Square

  7. 5. Solve by Completing the Square

  8. 6. Solve by Completing the Square

  9. The solutions of a quadratic equation in general form , when , are given by the quadratic formula: The Quadratic Formula

  10. 1. Write the equation in the form • 2. Determine the values of a, b, and c. • 3. Substitute the values of a, b, and c. into the quadratic formula and evaluate the expression. • 4. The sign indicates that there are two solutions of the equation. Steps to Solving the Quadratic Formula

  11. 7. Solve using the Quadratic Equation

  12. 8. Solve using the Quadratic Equation

  13. 9. Solve using the Quadratic Equation

  14. 10. Solve using the Quadratic Equation

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