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: ax 2 + 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 = 2x 2 +13 Graph it. What do you notice? Solve by factoring. What do you notice?

5. Solve by the quadratic formula 1. x 2 + 3x -2 = 02.x 2 = 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: ax 2 + bx + c = 0, the discriminant is: b 2 – 4ac

7. How to use the discriminant Value of the discriminant Number and nature of solutions. What this means graphically. b 2 – 4ac > 0 2 real solutions2 x-intercepts b 2 – 4ac = 0 1 real solutionTouches the graph, 1 x intercept b 2 – 4ac < 0 2 imaginary solutionsNo x –intercepts

8. Find the discriminant. Give the number and type of solutions of the equation. 1.9x 2 + 6x + 1 = 0 2. 9x 2 + 6x -4 = 0 3. 9x 2 + 6x +5 = 0

9. Vertical Motion Models h = -16t 2 + h o object is dropped h = -16t2 + v o t + h o object is launched or thrown Variables: h = height (feet) t = time (seconds) v o = initial velocity h o = 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?