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Review. How do we solve quadratic equations? 1.) Factoring using “ Bottoms Up ” 2.) if its not factorable by “ Completing the Square”. Quadratic Equations (2x 2 + 7x +5 = 0). Variable to the second power Graph is a parabola Solve by factoring if possible. +25. +25.

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Review

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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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