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Solving Quadratic Equations: Factoring, Completing the Square, and Quadratic Formula

Learn how to solve quadratic equations using factoring, completing the square, and the quadratic formula. Understand the discriminant and how it determines the number of solutions. Practice finding the roots of quadratic equations.

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Solving Quadratic Equations: Factoring, Completing the Square, and Quadratic Formula

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  1. Review • How do we solve quadratic equations? • 1.) Factoring using “Bottoms Up” • 2.) if its not factorable by “Completing the Square”

  2. Quadratic Equations(2x2 + 7x +5 = 0) • Variable to the second power • Graph is a parabola • Solve by factoring if possible

  3. +25 +25 Quadratic Equations(x2 + 10x +5 = 0) • Variable to the second power • Graph is a parabola • Solve by factoring if possible • If not factorable, use “complete the square” method

  4. 13.4 The Quadratic Formula • Objective: 1.)To use the quadratic formula to solve quadratic equations 2.) To use the discriminant to find the number of solutions for a quadratic equation

  5. Quadratic Formula The boy with the negative attitude couldn’t decide whether to go to the radical party or b² and miss out on the 4 awesome chicks the party is over at 2am

  6. Quadratic Song to Pop Goes the Weasel x equals negative b Plus or minus the square root Of b squared minus four a c All over 2a

  7. a b c 2 3 3 -7 -7 Quadratic Formula( 3 x2 –7 x + 2 = 0)

  8. 3x2 – 9x + 1 = 0

  9. 2x2– 5x - 6 = 0

  10. 2x2 + 7x – 4 = 0 2x2 = 4 – 7x

  11. 3x2 – 8 = 10x 3x2 - 10x – 8 = 0

  12. Discriminant Determines the number of real-number solutions of a quadratic equation b² - 4ac = discriminant

  13. Discriminant of a Quadratic3 possibilities b²-4ac 1.) If the discriminant is positive then the quadratic equations has 2 solutions for x 2.) If the discriminant is 0 then the quadratic has 1 solution for x 3.) If the discriminant is negative then there are no real solutions for x

  14. “discriminate” Negative: no solution Zero: one solution Positive: two solutions How many solutions?3x2 – 5x + 1 = 0 2 solutions

  15. “discriminate” Negative: no solution Zero: one solution Positive: two solutions How many solutions?y = x2 – 3x + 7 = 0 0 solutions

  16. “discriminate” Negative: no solution Zero: one solution Positive: two solutions How many solutions?f(x) = x2 – 12x + 36 = 0 1 solutions

  17. Solve: 3x2 – 4x - 2 = 0

  18. Solve: x2 - 4x - 7 = 0

  19. Assignment:Page 593# 2-28, 42-52finding the roots is the same as solving for x

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