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

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(22740) (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?

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