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10 January 2011

Explore the fundamental concepts of quadratic equations through examples and step-by-step instructions. This lesson covers how to find the vertex of a quadratic function and explains the process of solving quadratic equations by factoring. Learn the importance of identifying coefficients a, b, and c, and how to apply these concepts practically to solve equations like x² + 4x - 12 = 0. Gain confidence in algebra by mastering the techniques of finding x-intercepts and factoring polynomials effectively.

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10 January 2011

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  1. 10 January 2011 Algebra 2

  2. Bellringer • Find the vertex: f(x)=x2 + 10x – 5 • What are factors?

  3. Vocabulary • Vertex • Zero • X-intercept • Parabola

  4. Solving Quadratics by Factoring 1/10 If the quadratic equation is already factored, set each set of parentheses equal to zero, then solve for x (x + 5)(x – 2) = 0 Already Factored

  5. Solving Quadratics by Factoring 1/10 If the quadratic equation is already factored, set each set of parentheses equal to zero, then solve for x (x + 5)(x – 2) = 0 x + 5 = 0 x – 2 = 0 Already Factored

  6. Solving Quadratics by Factoring 1/10 If the quadratic equation is already factored, set each set of parentheses equal to zero, then solve for x (x + 5)(x – 2) = 0 x + 5 = 0 x – 2 = 0 - 5 - 5 + 2 + 2 Already Factored

  7. Solving Quadratics by Factoring 1/10 If the quadratic equation is already factored, set each set of parentheses equal to zero, then solve for x (x + 5)(x – 2) = 0 x + 5 = 0 x – 2 = 0 - 5 - 5 + 2 + 2 x = -5 x = 2 Already Factored

  8. Solving Quadratics by Factoring 1/10 If the quadratic equation is not factored, -Identify a,b,c x2 + 4x - 12= 0 Factor a Quadratic

  9. Solving Quadratics by Factoring 1/10 If the quadratic equation is not factored, -Identify a,b,c x2 + 4x - 12= 0 a b c Factor a Quadratic

  10. Solving Quadratics by Factoring 1/10 If the quadratic equation is not factored, -Identify a,b,c x2 + 4x - 12= 0 a b c a = 1 b = 4 c = -12 Factor a Quadratic

  11. Solving Quadratics by Factoring 1/10 If the quadratic equation is not factored, -Multiply a and c x2 + 4x - 12= 0 a = 1 c = -12 ac = -12 Factor a Quadratic

  12. Solving Quadratics by Factoring 1/10 If the quadratic equation is not factored, -Make a chart listing the factors of ac ac = -12 b = 4 Factor a Quadratic

  13. Solving Quadratics by Factoring 1/10 If the quadratic equation is not factored, -Add the a and c columns ac = -12 b = 4 Factor a Quadratic

  14. Solving Quadratics by Factoring 1/10 If the quadratic equation is not factored, -Add the a and c columns ac = -12 b = 4 Since b = 4, and 6 + -2 = 4, our factors are 6,-2. Factor a Quadratic

  15. Solving Quadratics by Factoring 1/10 x2 + 4x - 12= 0 Factors: 6,-2 Factor a Quadratic

  16. Solving Quadratics by Factoring 1/10 x2 + 4x - 12= 0 Factors: 6,-2 Factored Form: (x + 6)(x – 2) = 0 Factor a Quadratic

  17. Solving Quadratics by Factoring 1/10 x2 + 4x - 12= 0 Factors: 6,-2 Factored Form: (x + 6)(x – 2) = 0 Solve: x + 6 = 0 x – 2 = 0 Factor a Quadratic

  18. Solving Quadratics by Factoring 1/10 x2 + 4x - 12= 0 Factors: 6,-2 Factored Form: (x + 6)(x – 2) = 0 Solve: x + 6 = 0 x – 2 = 0 Final Answers: x = -6, 2 Factor a Quadratic

  19. Solving Quadratics by Factoring 1/10 Example 2 -Identify a,b,c x2 + 5x + 6= 0 Factor a Quadratic

  20. Solving Quadratics by Factoring 1/10 Example 2 -Identify a,b,c x2 + 5x + 6= 0 a b c Factor a Quadratic

  21. Solving Quadratics by Factoring 1/10 Example 2 -Identify a,b,c x2 + 5x + 6= 0 a b c a = 1 b = 5 c = 6 Factor a Quadratic

  22. Solving Quadratics by Factoring 1/10 Example 2: Multiply ac, and make a table ac = 6 b = 5 Factor a Quadratic

  23. Solving Quadratics by Factoring 1/10 Example 2: Multiply ac, and make a table ac = 6 b = 5 Factor a Quadratic

  24. Solving Quadratics by Factoring 1/10 Example 2: Multiply ac, and make a table ac = 6 b = 5 Factor a Quadratic

  25. Solving Quadratics by Factoring 1/10 Example 2: Multiply ac, and make a table ac = 6 b = 5 factors: 2,3 Factor a Quadratic

  26. Solving Quadratics by Factoring 1/10 Example 2 x2 + 5x + 6= 0 factors: 2,3 Factored Form: (x + 2)(x + 3) = 0 Factor a Quadratic

  27. Solving Quadratics by Factoring 1/10 Example 2 x2 + 5x + 6= 0 factors: 2,3 Factored Form: (x + 2)(x + 3) = 0 Solve: x + 2 = 0 x + 3 = 0 Factor a Quadratic

  28. Solving Quadratics by Factoring 1/10 Example 2 x2 + 5x + 6= 0 factors: 2,3 Factored Form: (x + 2)(x + 3) = 0 Solve: x + 2 = 0 x + 3 = 0 Final Answers: x = -2, -3 Factor a Quadratic

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