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Applications of the Vertex Formula,[object Object],Objective (4.3):Develop and apply a method for finding the maximum height of a projectile.,[object Object],SAT Problem of the day:,[object Object],The graph of a quadratic function y  is shown.  For what value of x does y  attain its greatest value?,[object Object],y = – x2 + 6x – 3,[object Object], 0.5,[object Object],(b)   3,[object Object],(c)   5.5,[object Object],(d)   6 ,[object Object],(e)  8,[object Object]
Vocabulary,[object Object],re-visited,[object Object],[object Object]
A parabola is the graph of a quadratic function.,[object Object]
	Thevertexof a parabola is either the lowest point on the graph or the highest point on the graph.,[object Object],Vertex ,[object Object],Vertex ,[object Object],book page 276,[object Object]
When a parabola opens up and the vertex,[object Object],is the lowest point the y-coordinate of the,[object Object],vertex is the minimum.,[object Object],maximum,[object Object],minimum,[object Object],When a parabola opens down and the,[object Object],vertex is the highest point the y-coordinate,[object Object],of the vertex is the maximum.,[object Object],book page 277,[object Object]
When a parabola opens up its lowest point is known as the:,[object Object],(a)minimum,[object Object],(b)maximum,[object Object],(c)vertex,[object Object],(d)a & c,[object Object],(e)b & c,[object Object],(f)all of the above,[object Object]
To help identify the vertex of a quadratic function we can use the following formula:,[object Object],– b,[object Object],2a,[object Object],x =,[object Object]
Where do we see quadratic functions in our everyday lives?,[object Object],pollanywhere.com ,[object Object]
Where do we see quadratic functions in real life?,[object Object]
What component do we often neglect when applying formulas for projectile motion?,[object Object],(a)initial height,[object Object],(b)initial velocity,[object Object],(c)height,[object Object],(d)air resistance	,[object Object],(e)velocity,[object Object]
Consider a firework display.,[object Object]
Collins Writing Type I:,[object Object],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?,[object Object],Time: 90 seconds                                 Length: 3 Lines,[object Object],http://www.online-stopwatch.com/large-stopwatch/,[object Object]
When a projectile is released into the air, what types of factors come into play?,[object Object],h = –16t2 + v0t + h0,[object Object],h0,[object Object],Initial Height,[object Object],Term used to represent the earth’s gravity.,[object Object],h,[object Object],Height,[object Object],t,[object Object],Time,[object Object],v0,[object Object],Initial Velocity (or speed),[object Object]
The path of a firework can be modeled using a quadratic function,[object Object],h = –16t2 + v0t + h0,[object Object],– b,[object Object],2a,[object Object],t=,[object Object],We can use the vertex formula to determine the time it takes for a firework to explode, and the maximum height that it reaches.,[object Object]
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.  ,[object Object],How long does it take for the fireworks to reach their maximum height?  ,[object Object],What is the maximum height reached by the fireworks?,[object Object],the football field,[object Object],initial velocity of 96,[object Object],How long ,[object Object],maximum height ,[object Object],h = –16t2 + v0t + h0,[object Object],– b,[object Object],2a,[object Object],t=,[object Object]
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.  ,[object Object],When will the fireworks reach their maximum height?  ,[object Object],What is the maximum height reached by the fireworks?,[object Object],80 feet tall,[object Object],initial velocity,[object Object],64 feet per second,[object Object],When,[object Object],maximum height ,[object Object],h = –16t2 + v0t + h0,[object Object],– b,[object Object],2a,[object Object],t=,[object Object]
Applications of the vertex formula edit
Textbook page 313,[object Object],Numbers 49 & 50,[object Object]
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.,[object Object],initial velocity,[object Object],of 48 feet per second,[object Object],6 feet above the ground,[object Object],maximum height ,[object Object],h = –16t2 + v0t + h0,[object Object],– b,[object Object],2a,[object Object],t=,[object Object]
EXIT TICKET ,[object Object],– b,[object Object],2a,[object Object],t=,[object Object],h = –16t2 + v0t + h0,[object Object]

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