1. Problem Solving Using the Discriminant

2. Quadratic Equation: 2 Discriminant: b 2 -4ac If b 2 -4ac is positive, then 2 solutions If b 2 -4ac is 0, then 1 solution If b 2 -4ac is negative, then no solution

3. If you find the discriminant, you can tell whether or not you will have a solution. Find the discriminant and number of solutions for: 3x 2 +4x-5=0 b 2 -4ac 4 2 -4(3)(-5) 16+60 76 2 Solutions x 2 -7x+16=0 b 2 -4ac (-7) 2 -4(1)(16) 49-64 -15 No Solution

4. Equations: Object dropped h=-16t 2 +s Object thrown h=-16t 2 +vt+s You are standing beneath a ledge that is 15 ft. high. If you throw a rope up at a velocity of 30 ft/sec., will it reach the ledge? Which equation? 15=-16t 2 +30t+0 0=-16t 2 +30t-15

5. Find discriminant to see if there is a solution before solving. b 2 -4ac 30 2 -4(-16)(-15) 900-960 -60 NO SOLUTION You must throw it harder

6. Try this one Rick is a firefighter and is leaning out a window on the eighth floor. He is trying to throw a grappling hook to a tenth-floor window that is 26 feet above him. Rick can throw the grappling hook with a maximum speed of 40 feet per second. Can he throw the grappling hook to the window above him?

7. Which formula do you need? h = -16t 2 + vt + s Plug in what you know and solve. 26 = -16t 2 + 40t + 0 0 = -16t 2 + 40t - 26 b 2 -4ac 40 2 – 4(-16)(-26) 1600 – 1664 -64

8. Answer: The discriminate is -64, so he cant throw it high enough. If he could throw it a little faster or if the window were a little closer, he could make it.