SOLUTION: Azim is the best basketball playerof all time.The height of his basketball shot from the top of his head is modeled by the function h(t)=-t^2+4t+6, h(t) us vertical displacement fr

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Question 831047: Azim is the best basketball playerof all time.The height of his basketball shot from the top of his head is modeled by the function h(t)=-t^2+4t+6, h(t) us vertical displacement from his head and t is is time in seconds. Azim is 6 feet tall and standing on the ground. What is the maximum height in feet that the ball will reach from the ground?
Found 2 solutions by nerdybill, brysca:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Azim is the best basketball playerof all time.The height of his basketball shot from the top of his head is modeled by the function h(t)=-t^2+4t+6, h(t) us vertical displacement from his head and t is is time in seconds. Azim is 6 feet tall and standing on the ground. What is the maximum height in feet that the ball will reach from the ground?
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h(t)=-t^2+4t+6
this is a "quadratic" (parabola) that opens downwards (from the coefficient associated with the first term).
This means the "vertex" will be at its maximum height.
The "time" at which it will reach this height is:
t = -b/(2a)
t = -4/(2*(-1))
t = -4/(-2)
t = 2 seconds
.
Height at this time, we plug it back into the original equation:
h(t)=-t^2+4t+6
h(2)=-2^2+4(2)+6
h(2)=-4+8+6
h(2)=4+6
h(2) = 10 feet (answer)

Answer by brysca(112) About Me  (Show Source):
You can put this solution on YOUR website!
If the graph is drawn out, it shows the trajectory of the basketball if it were to be shot by Azim.
The goal is to find the y value of the vertex in the equation, which will be the maximum height that the ball reaches.
Remember that the -%28t%5E2%29 part in the function is negative so the parabola is pointing downwards. Negative parabolas have maximums which is the vertex.
The expression for the vertex of a parabola is x+=+%28-b%29%2F%282%2Aa%29+.
So if you plug in the numbers corresponding to the equation it should look like this
%28-%284%29%29%2F%282%2A-1%29+ This should give you an answer of 2. Now, the expression for vertex is an equation for the x value of the vertex.
So, you need to find the y value. You do this by plugging 2 into the equation
h%28t%29=-t%5E2%2B4t%2B6%2C+h%28t%29 which would look like this
-%282%29%5E2%2B%284%2A2%29%2B6
Which gives you a y value of 10. The basketball will reach a maximum height of 10 feet.