The path of the diver is given by y= 4/9 x^2+24/9 x+12where y is the height in feet and x is the horizontal distance from the end of the diving board (in feet). What is the maximum height of the diver?

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Question:

The path of the diver is given by y= 4/9 x^2+24/9 x+12where y is the height in feet and x is the horizontal distance from the end of the diving board (in feet). What is the maximum height of the diver?

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Answer:Therefore the maximum height of the diver is 16 feet.Step-by-step explanation:The path of a driver is given by[tex]y=- \frac49 x^2+\frac{24}{9}x +12[/tex]where y is the height in feet and x is the horizontal distance.It is an equation of parabola.Here [tex]a = -\frac{4}{9}[/tex]  and  [tex]b= \frac{24}{9}[/tex]Since a<0 then the open side of the parabola is in downwards direction.The maximum height of the driver is the y-coordinate of vertex the parabola.The x-coordinate of the vertex [tex]=-\frac{b}{2a}[/tex]                                                    [tex]=-\frac{\frac{24}{9}}{2.(-\frac{4}9)}[/tex]                                                    [tex]= \frac{24}{8}[/tex]                                                    =3Putting the value of x in the given equation[tex]y=-\frac{4}{9}(3)^2+\frac{24}{9}.3+12[/tex]   = - 4+8+12   =16Therefore the coordinate of the vertex is = (3,16)Therefore the maximum height of the diver is 16 feet.  

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