SOLUTION: The path of a diver is given by the following, where y is the height (in feet) and x is the horizontal distance from the end of the diving board (in feet). y=-4/9 x^2 + 24/9 x + 1

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Question 805928: The path of a diver is given by the following, where y is the height (in feet) and x is the horizontal distance from the end of the diving board (in feet).
y=-4/9 x^2 + 24/9 x + 11
What is the maximum height of the diver?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=-%284%2F9%29+x%5E2+%2B+%2824%2F9%29+x+%2B+11..here you have parabola opened upside-down and maximum is at vertex; so, find coordinates of vertex
x=-b%2F2a will give us the x-coordinate of the vertex: b=%2824%2F9%29 and a=-%284%2F9%29
x=-%2824%2F9%29%2F2%28-%284%2F9%29%29
x=%28-24%2F9%29%2F%28-8%2F9%29
x=%28-24%2A9%29%2F%28-8%2A9%29
x=-24%2F-8
x=3
now plug it in equation and find y

y=-%284%2F9%293%5E2+%2B+%2824%2F9%29+3+%2B+11
y=-%284%2Fcross%289%29%29cross%289%29+%2B+%2824%2Fcross%289%293%29+cross%283%29+%2B+11
y=-4%2B+24%2F3++%2B+11
y=-4%2B+8++%2B+11
y=4++%2B+11
y=15
so, the vertex is at: (+3,15)
since given that y+ is the maximum height of the diver, it is +15ft