SOLUTION: If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t) = -16t^2 + 32t, wher

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t) = -16t^2 + 32t, wher      Log On


   

Question 149906: If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t) = -16t^2 + 32t, where t is time in seconds. What is the maximum height reached by the ball? Graph parabola 0<=t<=2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum height occurs at the vertex of the parabola. So let's find the vertex first




In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From y=-16t%5E2%2B32t, we can see that a=-16, b=32, and c=0.


x=%28-%2832%29%29%2F%282%28-16%29%29 Plug in a=-16 and b=32.


x=%28-32%29%2F%28-32%29 Multiply 2 and -16 to get -32.


x=1 Divide.


So the x-coordinate of the vertex is x=1. Note: this means that the axis of symmetry is also x=1.


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.


y=-16t%5E2%2B32t Start with the given equation.


y=-16t%5E2%2B32t Plug in x=1.


y=-16t%5E2%2B32t Start with the given equation.


y=-16%281%29%5E2%2B32%281%29 Plug in t=1.


y=-16%281%29%2B32%281%29 Square 1 to get 1.


y=-16%2B32%281%29 Multiply -16 and 1 to get -16.


y=-16%2B32 Multiply 32 and 1 to get 32.


y=16 Combine like terms.


So the y-coordinate of the vertex is y=16.


So the vertex is .


So the max height is 16 feet.



Now if we graph the equation y=-16t%5E2%2B32t on the interval , we can see that the highest point is (1,16). So this confirms our answer.


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