Question

you have been transported to a jungle-scape in the body of a mathematician. you build a catapult to launch messages to your team, who are on the other side of a deep and wide revine. the graph below shows the trajectory of your message. you launch the message 7 feet east of a tree that is 5 feet west of the edge of the revine. the ravine is 12 feet wide.

Answer 1

The trajectory of your message illustrates a quadratic function

The equation of the trajectory of the message is $y = -\frac 15(x - 17)^2 + 20$

How to determine the equation of the graph?

The trajectory graph (see attachment) is a quadratic function that passes through the following points:

(x,y) = (7,0) and (27,0)

And the vertex is:

(h,b) = (17,20)

A quadratic function is represented as:

$y = a(x - h)^2 + b$

So, we have:

$y = a(x - 17)^2 + 20$

Substitute (7,0) for (x,y)

$0 = a(7 - 17)^2 + 20$

Evaluate

$0 = 100a + 20$

Collect like terms

$100a = -20$

Divide both sides by 100

$a = -\frac 15$

Recall that:

$y = a(x - 17)^2 + 20$

So, we have:

$y = -\frac 15(x - 17)^2 + 20$

Hence, the equation of the trajectory of the message is $y = -\frac 15(x - 17)^2 + 20$

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