PLS HELP!!!! MEDAL AND FAN
Suppose that a water fountain produces a stream of water that follows the shape of a parabola. Assigning the origin of a coordinate system to the point where the water stream emerges from the fountain, a measurement shows that the maximum height of the stream occurs at the point (6, 5). Use symmetry to identify a third point and find a quadratic regression equation for the stream of water.

Question

PLS HELP!!!! MEDAL AND FAN
Suppose that a water fountain produces a stream of water that follows the shape of a parabola. Assigning the origin of a coordinate system to the point where the water stream emerges from the fountain, a measurement shows that the maximum height of the stream occurs at the point (6, 5). Use symmetry to identify a third point and find a quadratic regression equation for the stream of water.

anonymous · Answer

@ganeshie8

anonymous · Answer

@mathmate

imstuck · Answer

The point of its beginning is at the origin, right?  And it's vertex is (6,5)?  Is that what I am to understand thus far?

imstuck · Answer

The water would "land" at the point (12, 0), which is equidistant from the vertex but on the right side of it.  This parabola is of the -x^2 type because it opens downward, and has a vertex of (6,5) and roots of 0, 12.  Can you write the equation for the parabola using that info?

imstuck · Answer

Your final parabola has the standard equation of$$y=-.1388x ^{2}+1.6656x-1.6656$$

imstuck · Answer

Or if you round to the nearest thousandth and then multiply through by 1000 your would get this, which looks much nicer:$$y=-139x ^{2}+1666x-1666$$

anonymous · Answer

thanks a lot