SOLUTION: an archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t)= -16t.squared+ kt+ 3. If the maximum height of the arrow occurs at time t=

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: an archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t)= -16t.squared+ kt+ 3. If the maximum height of the arrow occurs at time t=      Log On


   

Question 163389: an archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t)= -16t.squared+ kt+ 3. If the maximum height of the arrow occurs at time t=4, what is the value of k?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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an archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t)= -16t.squared+ kt+ 3. If the maximum height of the arrow occurs at time t=4, what is the value of k?
:
We can use the axis of symmetry equation: x = %28-b%29%2F%282%2Aa%29
:
In this problem x = 4, a = -16, b = k
%28-k%29%2F%282%2A-16%29 = 4
%28-k%29%2F%28-32%29 = 4
a minus into a minus is a plus
k%2F32 = 4
Multiply both sides by 32
k = 32*4
k = 128