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Find the equation of the parabola that models the path of the water from the fireboat to the fire. The distance from the barrel of the water cannon to the roof of the warehouse is 180 feet and the water shoots up at maximum of 30 feet above the barrel of water cannon.
Vertex form of equation: y=A(x-h)^2+k, (h,k)=(x,y)coordinates of the vertex.
For given problem:
vertex: (0,30) (h=0, k=30)
coordinates of barrel of water cannon: (90,0) (right side of parabola)
solving for A using coordinates of cannon barrel and vertex
see graph below as a visual check: