SOLUTION: The height (h) of a baseball (t) seconds after being hit is given by h(t)= -16t^2 + 80t + 9. What is the height of the baseball when it is into the air? What is the maximum height

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Question 309225: The height (h) of a baseball (t) seconds after being hit is given by h(t)= -16t^2 + 80t + 9. What is the height of the baseball when it is into the air? What is the maximum height of the baseball and when does it reach this height? When does the baseball hit the ground?
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
The height (h) of a baseball (t) seconds after being hit is given by h(t)= -16t^2 + 80t + 9.
What is the height of the baseball when it is into the air?
The height is given by the equation:
h(t)= -16t^2 + 80t + 9
where
h(t) is the height
t is time in seconds
.
What is the maximum height of the baseball and when does it reach this height?
Maximum height is at the vertex:
t = -b/(2a) = -80/(2*(-16)) = 80/32 = 2.5
h(2.5) = -16(2.5^2) + 80(2.5) + 9 = 109 feet
When does the baseball hit the ground?
set h(t) to zero solve for t:
0 = -16t^2 + 80t + 9
Solve using the quadratic formula to get:
t = {-0.11, 5.11}
Throw out the negative solution leaving:
t = 5.11 secs
.
Details of quadratic :

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=6976 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.110076627227638, 5.11007662722764. Here's your graph: