1. Algebra 9.4 - The Quadratic Formula Objectives: Use the quadratic formula to solve a quadratic equation Why do you have to be a nonconformist like everybody else? James Thurber (1894 - 1961)

2. Solving Quadratics In 9.2 we learned to solve 3x 2 -48 = 0 3x 2 = 48 x 2 = 16 x =  4 The Quadratic Formula will allow us to solve any and every quadratic equation.

3. X= -b ± √b 2 -4ac 2a The song… The ‘other’ song….

4. Example 1 Solve using the quadratic formula 3y 2 +10= -11y +11y 3y 2 +11y +10= 0

7. Example 2 Find the value of b 2 -4ac

8. Example 3 Find the x-intercepts.

10. Quadratic Model in Real Life Object is dropped Object is thrown h=height(feet) t-=time in motion(seconds) s=initial height(feet) v=initial velocity(feet per second) v≠ speed

11. Example 4 Your brother is riding in a hot-air balloon over a lake. From an altitude of 4,000ft, he throws a rock straight down toward the water. When the rock leaves his hand, its speed is 30 feet per second. How long will it take the rock to hit the water?

12. 4,000ft- initial height Thrown at 30ft per sec.

13. However, does -16.8 second make sense? No, so the rock will hit the water about 14.9 seconds after it is throw.