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# Applications of the vertex formula edit

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### Applications of the vertex formula edit

1. 1. Applications of the Vertex Formula<br />Objective (4.3):Develop and apply a method for finding the maximum height of a projectile.<br />SAT Problem of the day:<br />The graph of a quadratic function y is shown. For what value of x does y attain its greatest value?<br />y = – x2 + 6x – 3<br /> 0.5<br />(b) 3<br />(c) 5.5<br />(d) 6 <br />(e) 8<br />
2. 2. Vocabulary<br />re-visited<br /><ul><li>A projectile is an object in which the only force acting upon it is gravity.
3. 3. A parabola is the graph of a quadratic function.</li></li></ul><li>Which of the following would NOT be considered aprojectile?<br />(a)Dropping a pumpkin off of a building.<br />(b)A plane taking off and then landing.<br />(c)Driving a golf ball.<br />(d)A person jumping on trampoline.<br />
4. 4. Thevertexof a parabola is either the lowest point on the graph or the highest point on the graph.<br />Vertex <br />Vertex <br />book page 276<br />
5. 5. When a parabola opens up and the vertex<br />is the lowest point the y-coordinate of the<br />vertex is the minimum.<br />maximum<br />minimum<br />When a parabola opens down and the<br />vertex is the highest point the y-coordinate<br />of the vertex is the maximum.<br />book page 277<br />
6. 6. When a parabola opens up its lowest point is known as the:<br />(a)minimum<br />(b)maximum<br />(c)vertex<br />(d)a & c<br />(e)b & c<br />(f)all of the above<br />
7. 7. To help identify the vertex of a quadratic function we can use the following formula:<br />– b<br />2a<br />x =<br />
8. 8. Where do we see quadratic functions in our everyday lives?<br />pollanywhere.com <br />
9. 9. Where do we see quadratic functions in real life?<br />
10. 10. What component do we often neglect when applying formulas for projectile motion?<br />(a)initial height<br />(b)initial velocity<br />(c)height<br />(d)air resistance <br />(e)velocity<br />
11. 11. Consider a firework display.<br />
12. 12. Collins Writing Type I:<br />When a projectile is released into the air a number of factors come into play including initial height, maximum height, time, and velocity. If you were designing a firework display why do you think each of these factors would be important?<br />Time: 90 seconds Length: 3 Lines<br />http://www.online-stopwatch.com/large-stopwatch/<br />
13. 13. When a projectile is released into the air, what types of factors come into play?<br />h = –16t2 + v0t + h0<br />h0<br />Initial Height<br />Term used to represent the earth’s gravity.<br />h<br />Height<br />t<br />Time<br />v0<br />Initial Velocity (or speed)<br />
14. 14. The path of a firework can be modeled using a quadratic function<br />h = –16t2 + v0t + h0<br />– b<br />2a<br />t=<br />We can use the vertex formula to determine the time it takes for a firework to explode, and the maximum height that it reaches.<br />
15. 15. On July 4th Ocean City has a firework display. The fireworks are ignited from the football field with an initial velocity of 96 feet per second. <br />How long does it take for the fireworks to reach their maximum height? <br />What is the maximum height reached by the fireworks?<br />the football field<br />initial velocity of 96<br />How long <br />maximum height <br />h = –16t2 + v0t + h0<br />– b<br />2a<br />t=<br />
16. 16. A professional pyro-technician shoots fireworks vertically into the air off of a building that is 80 feet tall. The initial velocity of the firework is 64 feet per second. <br />When will the fireworks reach their maximum height? <br />What is the maximum height reached by the fireworks?<br />80 feet tall<br />initial velocity<br />64 feet per second<br />When<br />maximum height <br />h = –16t2 + v0t + h0<br />– b<br />2a<br />t=<br />
17. 17.
18. 18. Textbook page 313<br />Numbers 49 & 50<br />
19. 19. A baseball is thrown upward with an initial velocity of 48 feet per second from 6 feet above the ground. Determine the maximum height of the ball.<br />initial velocity<br />of 48 feet per second<br />6 feet above the ground<br />maximum height <br />h = –16t2 + v0t + h0<br />– b<br />2a<br />t=<br />
20. 20. EXIT TICKET <br />– b<br />2a<br />t=<br />h = –16t2 + v0t + h0<br />