Hot Air Balloon Hot Air Balloon InvestigationInvestigation

PPT 5.3.1

Introduction

Two students, Ginger and Paul, were going on a hot air balloon trip to see what it was like.

Their trip can be described by the function h(t) = -1.252t4 + 10.732t3 – 30.377t2 +29.931t

where the height, h metres, of the balloon is relative to the ground for t hours.

Graph the Trip

We are going to graph the equation given on the previous slide on your graphing calculator.

Before we enter the equation, we are going to change your WINDOW settings.

WINDOW Settings• Since time is along the x-axis,

and we don’t have a negative time, set X MIN = 0.

• The ride will most likely not take more than 5 hours, so set X MAX = 5.

• Since the height of the balloon is relative to the ground, we would not expect it to go below the ground level, so we can set Y MIN = 0.

Your screen should look like the one on the right.

Graph it!

Okay, now we are ready to graph the equation.

Press the Y = button and type in the following:

-1.252x^4+10.732x^3-30.377x^2+29.931x

Press the GRAPH button.

Your screen should look like the one on the right.

What Does the Graph Show Us?

The graph starts off at the origin. Why?

Approximately, what is the maximum height that the hot air balloon reaches?

Describe what is happening on the trip from the beginning to the end.

At what time did the balloon reach it’s maximum height?

How long did the trip last? How do you know?

What type of function would be the best to describe this graph?