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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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