Question

2. A paper airplane was thrown from the top of a tall building. The height of the paper airplane above the ground can be found using the function f(x) = −1.5x + 69, where x is the time in seconds the airplane has been in the air.

a. Draw the graph of the function

b. How many seconds did it take the paper airplane to reach the ground?

c. Explain your answer.

Answer 1

Part a) The graph in the attached figure

Part b) It takes the paper airplane 46 seconds to get to the ground.

Explanation:

we have

`f(x) =-1.5x + 69`

where

x -----> x is the time in seconds the airplane has been in the air.

f(x) ----> the height of the paper airplane above the ground

Part a) Draw the graph of the function

This is a linear function (is a line)

To graph the line plot the intercepts and join the points

Find the y-intercept

The y-intercept is the value of the function f(x) when the value of x is equal to zero

For x=0

`f(x) =-1.5(0) + 69=69`

The y-intercept is the point (0,69)

Find the x-intercept

The x-intercept is the value of x when the value of the function is equal to zero

For f(x)=0

`0=-1.5x + 69`

`1.5x=69`

`x=69/1.5`

`x=46`

The x-intercept is the point (46,0)

using a graphing tool

Plot the points (0,69) and (46,0) and join to graph the line

see the attached figure

Part b) How many seconds did it take the paper airplane to reach the ground?

we know that

When the paper airplane reach the ground, the height is equal to zero

so

Determine the x-intercept

For f(x)=0

`0=-1.5x + 69`

`1.5x=69`

`x=69/1.5`

`x=46`

The x-intercept is the point (46,0)

therefore

It takes the paper airplane 46 seconds to get to the ground.