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5.6: The Quadratic Formula and the Discriminant

5.6: The Quadratic Formula and the Discriminant. Objectives: Students will be able to… Solve a quadratic equation using the quadratic formula Use the discriminant to determine the number of solutions a quadratic equation has. The Quadratic Formula!!!.

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5.6: The Quadratic Formula and the Discriminant

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  1. 5.6: The Quadratic Formula and the Discriminant Objectives: Students will be able to… Solve a quadratic equation using the quadratic formula Use the discriminant to determine the number of solutions a quadratic equation has

  2. The Quadratic Formula!!! • Works to solve every quadratic equation in standard form: ax2 + bx + c= 0, a ≠ 0 (must set equation equal to 0 first!!) IT’S MAGIC!!!

  3. Solve using the quadratic formula. Now graph the equation and check!! Then solve by factoring!!

  4. Solve using the quadratic formula. 12x-5 = 2x2 +13 Graph it. What do you notice? Solve by factoring. What do you notice?

  5. Solve by the quadratic formula 1. x2 + 3x -2 = 0 • x2 = 2x – 5 Graph it. What do you notice?

  6. The Discriminant • Tells us how many solutions a quadratic equation has and the nature of them (real or imaginary) When you have a quadratic equation in standard form: ax2 + bx + c = 0, the discriminant is: b2 – 4ac

  7. How to use the discriminant

  8. Find the discriminant. Give the number and type of solutions of the equation. • 9x2+ 6x + 1 = 0 2. 9x2+ 6x -4 = 0 3. 9x2+ 6x +5 = 0

  9. Vertical Motion Models h = -16t2 + ho object is dropped h = -16t2 + vot + ho object is launched or thrown Variables: h = height (feet) t = time (seconds) vo = initial velocity ho = initial height

  10. The water in a large fountain leaves the spout with a vertical velocity of 30 ft per second. After going up in the air, it lands in a basin 6 ft below the spout. If the spout is 10 ft above the ground, how long does it take a single drop of water to travel from the spout to the basin?

  11. A man tosses a penny up into the air above a 100 ft deep well with a velocity of 5 ft/sec. The penny leaves the man’s hand at a height of 4 ft. How long will it take the penny to reach the bottom of the well?

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