solving systems of equations graphically

Question

as part of a fountain display,  to jets of water travel from the surface of an upper pool and meet at the service of a lower pool.  The paths of the two jets are modelled by y=-x² -4x and y=-3x² -15x, where x and y are measured in feet. What is the vertical height difference, d, of the pools? Round your answer to the nearest hundredth 

Answer 1

To solve the problem graphically, you just need to graph both equations and find the maxima of the equation.

 

However, you can find the maxima of both equations mathematically by using the equation maxima= c-(b²/4a)

 

For Jet 1 where y1=-x²-4x    maxima= 0- (4²/4*1)= -16/4= -4

 

For Jet 2 where y2=-3x²-15x maxima=0-(15²/4*3)= 225/12= 75/4= 18.75=-18.8

 

The height difference is just the difference of the maxima:

 

height difference= 18.8-4= 14.8 ft