Question 1181254
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This problem is advanced, which means that it is above the average high school level.


So, I will assume that my visitor has an adequate level in Math (otherwise, there is no sense in discussing).



            The idea is that the base of the triangle is just given: 
            it is the segment AB, whose length you can easily calculate.


            So, our task is to find the point P on the parabola, 
            which provides minimum height (i.e. altitude) of the triangle.



It is the same as to say that our task is to find the point P on the parabola, CLOSEST to the line through the points A and B.



I solved a TWIN problem TODAY under this link


https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1181253.html



Having this solution as a TEMPLATE, complete the solution to this problem to the end on your own.



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Oops, it looks like Edwin just made everything I described in my post.