Question

A group of students launches a model rocket from the top of a building. The
students have determined the equation y = − ;
(x+ 6)(x − 18) to describe the
<
height of the rocket above ground level, y, in metres, at any time, x, in seconds. Graph your results.

Answer 1

As an AI language model, I cannot provide a graph. However, I can explain the steps to graph the equation.

To graph the equation y = -1/[(x+6)(x-18)], we can follow these steps:

1. Determine the range of x-values for the graph. Let's choose x-values from -10 to 20, since the rocket is launched at time 0 and it will hit the ground again after 18 seconds.

2. Calculate the y-values for each x-value using the equation. For example, when x = 0, y = -1/[(-6)(18)] = 1/108. When x = 10, y = -1/[(10+6)(10-18)] = -1/64.

3. Plot the points (x,y) on a graph paper. Use a scale that fits the range of x and y values you have chosen.

4. Connect the dots with a smooth curve to show the trend of the function. Remember that the function approaches zero as x approaches infinity, and that it has vertical asymptotes at x = -6 and x = 18.

The final graph should look like a hyperbola that approaches zero on the right and left sides, and has two vertical asymptotes at x = -6 and x = 18.