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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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) About Me  (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 = -4%2F9x^2 + 24%2F9x + 12
:
Find the axis of symmetry using the formula: x =-b/(2a); a=-4/9; b=24/9
x = %28-24%2F9%29%2F%282%2A%28-4%2F9%29%29 = %28-24%2F9%29%2F%28%28-8%2F9%29%29
Invert the dividing fraction and multiply
x = %28-24%2F9%29%2A%28-9%2F8%29 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 = -4%2F93^2 + 24%2F93 + 12
:
y = -4%2F99 + 72%2F9 + 12
cancel
y = -4 + 8 + 12
:
y = 16 ft is max height
:
:
A graph of this equation will make it clear:
+graph%28+300%2C+200%2C+-6%2C+12%2C+-10%2C+20%2C+%28-4%2F9%29x%5E2%2B%2824%2F9%29x%2B12%29+
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?