SOLUTION: Please help me solve this: A penny is thrown up in the air from a building. Its height in feet after x seconds is given by: {{{ -16x^2 +24x+75 }}} a) when does it reach it's max h

Question 930432: Please help me solve this: A penny is thrown up in the air from a building. Its height in feet after x seconds is given by:
a) when does it reach it's max height?
b) what is its max height?
c) when does it hit the ground?
For (c) I started to solve it with the quadratic formula but wasn't getting a sensible answer. I'm not sure how to set up the other two.

Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A penny is thrown up in the air from a building. Its height in feet after x seconds is given by:
a) when does it reach it's [sic] max height?
It's the vertex of the parabola, at x = -b/2a
x = -24/-32 seconds = 3/4 seconds
--------------------------------
b) what is its max height?
h(x) = -16*(3/4)^2 + 24*(3/4) + 75
= -9 + 18 + 75
= 84 ft
-------------------------
c) when does it hit the ground?

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=5376 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -1.54128784747792, 3.04128784747792. Here's your graph:

Ignore the negative solution.
x =~ 3.041 seconds
For (c) I started to solve it with the quadratic formula but wasn't getting a sensible answer. I'm not sure how to set up the other two.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
a) The maximum for a quadratic function
happens at .
In this case, ,
so it reaches maximum height at seconds.

b) At that point, the height in feet is
feet.

c) is an equation I would solve by "completing the square".

Since the other solution is negative, the only solution that makes sense is:

seconds (rounded).

USING THE QUADRATIC FORMULA, the calculation becomes a bit more painful:
The quadratic formula says that the solutions to are given by

In this case, with , , and ,
so

Approximating, we get

The negative solution does not make sense.
The positive solution is

seconds (rounded).
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