A canopy tour company designs zip line rides through forest and jungle environments. One particular zip line takes the passenger through a waterfall, the maximum height of which is 167 ft. The dimensions of both the zip line and the waterfall are shown in the image below.
The waterfall is a parabola....let its vertex be (0, 167)
And the point (75,0) is on the parabola
Using the vertex form we can find "a:" thusly
0 = a ( 75 - 0)^2 + 167
0 = a (75)^2 + 167
-167 / ( 75^2) = a = -167 / 5625
So.....the equation for the waterfall is :
y = (-167 / 5625) x^2 + 167
The zipline is a straight line with points (0, 130) qnd (100, 0) on the line
Its slope is [ -130 / 100] = -13/10
Its equation is
y = (-13/10)x + 130