SOLUTION: A baseball is hit at a point 3 ft above the ground at a velocity of 100ft/s and at an angle of 45 degrees with respect of the ground. The path of the baseball is given by the funct

Question 165101: A baseball is hit at a point 3 ft above the ground at a velocity of 100ft/s and at an angle of 45 degrees with respect of the ground. The path of the baseball is given by the function f(x) = -0.0032x2 + x +3 where f(x) is the height of the baseball (in feet) and x is the horizontal distance from home plate (in feet). What's the maximum hieght reached by the baseball?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, the max height occurs at the vertex. So if we find the y-coordinate of the vertex, we find the max height.

Note: the same applies to the min height (if there exists a min height)

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.

Divide

So the x-coordinate of the vertex is .

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 .

Square to get .

Multiply

Combine like terms.

So the y-coordinate of the vertex is .

So the vertex is (156.25,81.125).

Since the y-coordinate is , this means that the max height is 81.125 ft.

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