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

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) (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: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Multiply 2 and to get .

Divide.

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

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

Start with the given equation.

Plug in .

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

So the vertex is

.

So the max height is 16 feet.

Now if we graph the equation on the interval

, we can see that the highest point is (1,16). So this confirms our answer.

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