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A fountain in a shopping mall has two parabolic arcs of water intersecting in one point.
The equation of one parabola is y= -0.25x^2+2x and the equation of the second parabola is y= -0.25x^2+4.5x.
How high above the base of the fountain do the parabolas intersect?
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y = (1)
y = (2)
Since the left sides in (1) and (2) are equal at some x, we can equate the right sides to find x:
= .
Simplify. Cancel the terms in both sides. You will get
2x = 4.5x ====> 4.5x - 2x = 0 ====> (4.5-2)*x = 0 ====> x = 0.
So, the only solution is x = 0.
Then y = 0.
Answer. The only intersection point is (x,y) = (0,0).
If this solution seems to be incorrect to you, double check and revise you condition.