1. Do NOW
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7.4a - Change of Base

2. Worksheet Key
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7.4a - Change of Base

3. Quadratic Applications
Section 7.4A, Revised ©2013,
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7.4a - Change of Base

4. Quadratic Equations
Quadratic Equation is y = ax2 + bx + c where as a, b, and c are numbers
Vertex Equation: x = –b/2a and plug in x to get y
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7.4a - Change of Base

5. Quadratic Applications
Read the question TWICE
Understand the Question
Underline key numbers and terms
Plug in equation using the graphing calculator
When graphing, ALWAYS label the x and y-axis (Remember: y depends on x)
Plot out the points from the graphing calculator
Connect the points and make the parabola
Establish the Vertex, Axis of Symmetry, and Zeros
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7.4a - Change of Base

6. Example 1
A soccer player kicked a ball whose height can be modeled by the equation, h = –16t2 + 128t, where h is height in feet and t is time in seconds.  How long does it take for the ball to reach the ground? How high did it go and for how many seconds?
How long does it take for the ball to reach the ground?
Use the graphing calculator to fill in the table. x y 1
112 2
192 3
240 4
256 5 6 7 8 x y 1 2 3 4 5 6 7 8
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7.4a - Change of Base

7. Example 1
A soccer player kicked a ball whose height can be modeled by the equation, h = –16t2 + 128t, where h is height in feet and t is time in seconds.  How long does it take for the ball to reach the ground? How high did it go and for how many seconds?
Use the table to Plot and Graph the Points
How long does it take?
How high does it go?
For the y-axis let each interval be 40 ft x y 1
112 2
192 3
240 4
256 5 6 7 8
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7.4a - Change of Base

8. Example 2
Scott shot his algebra book using a giant slingshot. The path of the book can be modeled by the function h = –16t2 +96t where h is the height and t is time.   Graph the function. How long does it take for the book to reach the ground? How high did it go and for how many seconds? x y 1
144 2
256 3
336 4
384 5
400 6 7 8 9 10 x y 1 2 3 4 5 6 7 8 9 10
How long does it take?
How high does it go?
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7.4a - Change of Base

9. Your Turn
James was playing basketball where is was trying to make a three-pointer. The path of the ball can be modeled by the function, h = –16t2 + 96t where h is the height and t is time.   Graph the function. How long does it take for the ball to reach the ground? How high did it go and at for how many seconds?
How long does it take?
How high does it go? x y 1 80 2
128 3
144 4 5 6 x y 1 2 3 4 5 6
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7.4a - Change of Base

10. Example 3
During practice, a hockey player was hitting the puck whereas the height can be modeled by the equation, h = –16t2 + 144t, where h is height in feet and t is time in seconds.  How high did it go and for how many seconds?
How long does it take for the ball to reach the ground?
Use the graphing calculator to fill in the table. x y 1
128 2
224 3
288 4
320 5 6 7 8 9 x y 1 2 3 4 5 6 7 8 9
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7.4a - Change of Base

11. What is the vertex if it isn’t given in our calculator table?
Example 3
During practice, a hockey player was hitting the puck whereas the height can be modeled by the equation, h = –16t2 + 144t, where h is height in feet and t is time in seconds.  How high did it go and for how many seconds?
What is the vertex if it isn’t given in our calculator table? x y 1
128 2
224 3
288 4
320 5 6 7 8 9 x y 1 2 3 4 5 6 7 8 9
2/19/2019 6:15 AM
7.4a - Change of Base

12. What is the vertex if it isn’t given in our calculator table?
Example 3
During practice, a hockey player was hitting the puck whereas the height can be modeled by the equation, h = –16t2 + 144t, where h is height in feet and t is time in seconds.  How high did it go and for how many seconds?
What is the vertex if it isn’t given in our calculator table? x y 1
128 2
224 3
288 4
320 5 6 7 8 9 x y 1 2 3 4 5 6 7 8 9
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7.4a - Change of Base

13. Example 4
During practice, a softball pitcher throws a ball whose height can be modeled by the equation, h = –16t2 + 24t + 1, where h is height in feet and t is time in seconds. How high did it go and for how many seconds?
7.4a - Change of Base

14. Your Turn
An athlete throws a shot put with an initial velocity of 40 feet per second. The equation that models the height is as follows: h = –16t2 + 40t + 6.5, where h is height in feet and t is time in seconds. How high did it go and for how many seconds?
7.4a - Change of Base

15. Assignment
Worksheet
7.4a - Change of Base