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Thinking Mathematically

Thinking Mathematically. Algebra: Equations and Inequalities 6.6 Solving Quadratic Equations. Definition of a Quadratic Equation. A quadratic equation in x is an equation that can be written in the general form ax 2 + bx + c = 0, where a, b, and c are real numbers, with a ≠0 .

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Thinking Mathematically

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  1. Thinking Mathematically Algebra: Equations and Inequalities 6.6 Solving Quadratic Equations

  2. Definition of a Quadratic Equation A quadratic equation in x is an equation that can be written in the general form ax2 + bx + c = 0, where a, b, and c are real numbers, with a≠0. Linear vs. quadratic

  3. Using the FOIL Method to Multiply Binomials (ax + b)(cx +d) = ax•cx + ax•d + b•cx + b•d = acx2 + (ad + dc)x + bd F: First terms (x2 term) O: Outside terms (x term) I: Inside terms (x term) L: Last terms (constant term) An application of the Distributive Property

  4. Example: Multiplying Binomials Exercise Set 6.6 #3 (x - 5)(x + 3)

  5. Factoring a Trinomial • The inverse of FOIL • Exercise Set 6.6 #11, #13, #17, #21 • x2 -2x - 15 • x2 – 8x + 15 • x2 – 8x + 32 • 2x2 + 7x + 3

  6. The Zero-Product Principle If the product of two factors is zero, then one (or both) of the factors must have a value of zero. If A•B = 0, then A = 0 or B = 0. Solution set contains two answers.

  7. Solving a Quadratic Equation Using the Zero-Product Principle • Exercise Set 6.6 #33 • (x – 8)(x + 3) = 0

  8. Using Factoring to Solve a Quadratic Equation • Exercise Set 6.6 #37, 41 • x2 + 8x + 15 = 0 • x2 – 4x = 21

  9. Thinking Mathematically Algebra: Equations and Inequalities 6.6 Solving Quadratic Equations

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