In section 1, you used the height function h(t) = -16t² + c  to determine the height of a falling object after t seconds.  This function, however, works only for objects falling here on Earth.   What happens if we were on another planet?

In this function, -16 represent the gravitational force in feet here on Earth.  Relating the height function and the quadratic function again, f(x) = a(x − h)²+ k

Which variable of the quadratic function would change if the gravitational force was different?

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If the gravitational force was different from Earth’s 16 ft/sec, it would change the “a” value in the quadratic height function.

Example 2

Jupiter has the strongest gravitational forces of all the planets. Its height function for an egg that drops 20 feet is represented by h_J(t) = -41x² + 20.

1. Use your own graphing paper or click on the image below to use an online graph plotter to graph the function of the egg that drops from 20 feet on Earth, f(x) = -16x² + 20 as well as the function of the egg that drops from 20 feet on Jupiter, f(x) = -41x²+ 20 on the same coordinate (x,y) grid.
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Directions on how to enter the equations and set a good window for the graph.
To enter in your equations you must use the asterisk “*” for multiplication and “^” for an exponent. Here is how to enter the first graph. -16*x^2+20. To create a good viewing window change the range of the x-axis values from -5 and 5 to -2 and 2. Also change the range of the y-axis values from -5 and 5 to -25 and 25. Click on Draw or hit Enter to create the graphs.




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2. What type of translation occurred in this problem?
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Since the red graph is narrower than the blue graph, there is a vertical stretch between the graphs that represent the egg dropping on Earth and the egg that drops on Jupiter.

3. What is the meaning of this translation?
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Both eggs drop from a height of 20 feet, but the egg on Jupiter will hit the ground 2 and a half times (-41/-16) faster than the egg dropped on Earth.

In this section, you discovered that dropping an object with different gravitational forces resulted in a stretching. In the next section, you will investigate problems about maximum area.