Question 1091797
.
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?
~~~~~~~~~~~~~~~~~


<pre>
 y = {{{-0.25x^2 + 2x}}}       (1)

 y = {{{-0.25x^2 + 4.5x}}}     (2)


Since the left sides in (1) and (2) are equal at some x, we can equate the right sides to find x:

{{{-0.25x^2 + 2x}}}  = {{{-0.25x^2 + 4.5x}}}.


Simplify. Cancel the terms {{{-0.25x^2}}} 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.


<U>Answer</U>.  The only intersection point is  (x,y) = (0,0).
</pre>

If this solution seems to be incorrect to you, double check and revise you condition.