Question

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.

Answer 1

The quadratic regression equation for the stream of water is $y=-0.139x^{2} +1.667x$ {parabola}

     

Given that the water stream produced by fountain is parabola

Vertex of parabola is (6,5) , parbola is facing downward,axis of symmetry of parabola is x=6 and parabola passes through (0,0)

according to symmetry the third point on the parabola is (12,0)

General equation for a parabola⇒ Y=-4a$X^{2}$

⇒(y-5)=-4a$(x-6)^{2}$    { as the Vertex of parabola is (6,5) }

⇒(y-5)=-4a($x^{2} +36-12x$)

subtituting (0,0) in the equation to get the value of a

⇒-5=-4a(36)

⇒ a=$\frac{-5}{144}$                      

equation of parabola⇒(y-5)=-4( $\frac{5}{144}$)$(x-6)^{2}$

Therefore,The quadratic regression equation for the stream of water is $y=-0.139x^{2} +1.667x$

Learn more about parabola here:

brainly.com/question/21685473

#SPJ4