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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.

Respuesta :

The quadratic regression equation for the stream of water is [tex]y=-0.139x^{2} +1.667x[/tex] {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[tex]X^{2}[/tex]

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

⇒(y-5)=-4a([tex]x^{2} +36-12x[/tex])

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

⇒-5=-4a(36)

⇒ a=[tex]\frac{-5}{144}[/tex]                      

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

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

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