example 3 height of a ball chapter 3.1 a ball is thrown at 64 feet per second from the top of an...
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![Page 1: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/1.jpg)
example 3 Height of a Ball
Chapter 3.1
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
a. Write the quadratic function that models the height (in feet) of the ball as a function of the time t (in seconds).
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
c. Graph the model.
d. Explain the meaning of the coordinates of the vertex for this model.
2009 PBLPathways
![Page 2: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/2.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
a. Write the quadratic function that models the height (in feet) of the ball as a function of the time t (in seconds).
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
c. Graph the model.
d. Explain the meaning of the coordinates of the vertex for this model.
![Page 3: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/3.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
a. Write the quadratic function that models the height (in feet) of the ball as a function of the time t (in seconds).
20 016S t v t h 216 64 80S t t
v0 is the initial speed (at t = 0) in feet per second
h0 is the initial height (at t = 0) in feet
-16 feet per second2 is the acceleration due to gravity
v0 = 64 h0 = 80
![Page 4: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/4.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
a. Write the quadratic function that models the height (in feet) of the ball as a function of the time t (in seconds).
20 016S t v t h 216 64 80S t t
v0 is the initial speed (at t = 0) in feet per second
h0 is the initial height (at t = 0) in feet
-16 feet per second2 is the acceleration due to gravity
v0 = 64 h0 = 80
![Page 5: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/5.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
a. Write the quadratic function that models the height (in feet) of the ball as a function of the time t (in seconds).
20 016S t v t h 216 64 80S t t
v0 is the initial speed (at t = 0) in feet per second
h0 is the initial height (at t = 0) in feet
-16 feet per second2 is the acceleration due to gravity
v0 = 64 h0 = 80
![Page 6: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/6.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
a. Write the quadratic function that models the height (in feet) of the ball as a function of the time t (in seconds).
20 016S t v t h 216 64 80S t t
v0 is the initial speed (at t = 0) in feet per second
h0 is the initial height (at t = 0) in feet
-16 feet per second2 is the acceleration due to gravity
v0 = 64 h0 = 80
![Page 7: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/7.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
a. Write the quadratic function that models the height (in feet) of the ball as a function of the time t (in seconds).
20 016S t v t h 216 64 80S t t
v0 is the initial speed (at t = 0) in feet per second
h0 is the initial height (at t = 0) in feet
-16 feet per second2 is the acceleration due to gravity
v0 = 64 h0 = 80
![Page 8: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/8.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
a. Write the quadratic function that models the height (in feet) of the ball as a function of the time t (in seconds).
20 016S t v t h 216 64 80S t t
v0 is the initial speed (at t = 0) in feet per second
h0 is the initial height (at t = 0) in feet
-16 feet per second2 is the acceleration due to gravity
v0 = 64 h0 = 80
![Page 9: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/9.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
64
22 2 16
bt
a
2
2
16 64 80
16 2 64 2 80
144
S t t
![Page 10: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/10.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
64
22 2 16
bt
a
2
2
16 64 80
16 2 64 2 80
144
S t t
![Page 11: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/11.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
64
22 2 16
bt
a
2
2
16 64 80
16 2 64 2 80
144
S t t
![Page 12: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/12.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
64
22 2 16
bt
a
2
2
16 64 80
16 2 64 2 80
144
S t t
![Page 13: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/13.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
64
22 2 16
bt
a
2
2
16 64 80
16 2 64 2 80
144
S t t
![Page 14: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/14.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
64
22 2 16
bt
a
2
2
16 64 80
16 2 64 2 80
144
S t t
![Page 15: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/15.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
64
22 2 16
bt
a
2
2
16 64 80
16 2 64 2 80
144
S t t
![Page 16: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/16.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
b. Find the t-coordinate and s-coordinate of the vertex of the graph of this quadratic function.
64
22 2 16
bt
a
2
2
16 64 80
16 2 64 2 80
144
S t t
![Page 17: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/17.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
c. Graph the model.
t
S (2, 144)
216 64 80S t t
![Page 18: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/18.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
c. Graph the model.
t
S (2, 144)
216 64 80S t t
![Page 19: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/19.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
d. Explain the meaning of the coordinates of the vertex for this model.
t
S (2, 144)
216 64 80S t t
![Page 20: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/20.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
d. Explain the meaning of the coordinates of the vertex for this model.
t
S (2, 144)
216 64 80S t t
![Page 21: Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function](https://reader030.vdocuments.net/reader030/viewer/2022032805/56649ee85503460f94bf94db/html5/thumbnails/21.jpg)
2009 PBLPathways
A ball is thrown at 64 feet per second from the top of an 80-foot-high building.
d. Explain the meaning of the coordinates of the vertex for this model.
t
S (2, 144)144
216 64 80S t t