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

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 Click here to see ALL problems on Miscellaneous Word Problems Question 147130: The path of the diver is given by y= 4/9 x^2+24/9 x+12 where 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? Thank you for any help here.Answer by ankor@dixie-net.com(15660)   (Show Source): You can put this solution on YOUR website!The path of the diver is given by y= 4/9x^2 + 24/9x + 12 where y is the height in feet x is the horizontal distance from the end of the diving board (in feet). : The coefficient of x^2 has to be negative to have a maximum, assuming the equation is: y = x^2 + x + 12 : Find the axis of symmetry using the formula: x =-b/(2a); a=-4/9; b=24/9 x = = Invert the dividing fraction and multiply x = cancel and you have: x = +3 ft horizontal distance from end of diving board for max height : What is the maximum height of the diver? : Substitute 3 for x in the original equation to find max height y = 3^2 + 3 + 12 : y = 9 + + 12 cancel y = -4 + 8 + 12 : y = 16 ft is max height : : A graph of this equation will make it clear: Note this also shows the diving board to be 12 ft above the water and he will enter the water 9 ft from the end of the diving board. : : Did this make some sense to you?