SOLUTION: A fountain in a shopping mall has two parabolic arcs of water intersecting. The equation of one parabola is y=-0.25x^2+2x and the equation of the second parabola is y=-0.25x^2+4x-1

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A fountain in a shopping mall has two parabolic arcs of water intersecting. The equation of one parabola is y=-0.25x^2+2x and the equation of the second parabola is y=-0.25x^2+4x-1      Log On


   

Question 607483: A fountain in a shopping mall has two parabolic arcs of water intersecting. The equation of one parabola is y=-0.25x^2+2x and the equation of the second parabola is y=-0.25x^2+4x-11.75. How high above the base of the fountain do the parabolas intersect: All dimensions are in feet. Round to the nearest hundredth.
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A fountain in a shopping mall has two parabolic arcs of water intersecting. The equation of one parabola is y=-0.25x^2+2x and the equation of the second parabola is y=-0.25x^2+4x-11.75. How high above the base of the fountain do the parabolas intersect: All dimensions are in feet. Round to the nearest hundredth.
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When parabolas intersect, the equations are equal to each other.
-0.25x^2+2x=-0.25x^2+4x-11.75
2x=11.75
x=11.75/2=5.875
y=-.25*(5.875)^2+2*5.875=3.121 ft
ans:
parabolas intersect 3.121 ft above the base