SOLUTION: Can you please help my in How to solve quadratic function word problems my question is A ball is released 6 feet above the ground and thrown vertically into the air. The equation

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Question 604841: Can you please help my in How to solve quadratic function word problems
my question is
A ball is released 6 feet above the ground and thrown vertically into the air. The equation h=-16t^+112t+6 gives the height of the ball if the initial is 112 feet per second.
1. Write the equation of the axis of symmetry and find the coordinates of the vertex of the graph of the equation.
2. What is the maximum height above the ground that the ball reaches?
3. How many seconds is the ball in the air?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A ball is released 6 feet above the ground and thrown vertically into the air. The equation h=-16t^+112t+6 gives the height of the ball if the initial is 112 feet per second.
1. Write the equation of the axis of symmetry and find the coordinates of the vertex of the graph of the equation.
.
axis of symmetry:
x = -b/(2a)
x = -112/(2(-16))
x = -112/(-32)
x = 3.5 (vertical line crossing at x=3.5)
.
find, y-value when x=3.5:
-16t^+112t+6
-16(3.5)^+112(3.5)+6
202
So, vertex is at (3.5, 202)
.
2. What is the maximum height above the ground that the ball reaches?
202 feet
3. How many seconds is the ball in the air?
set h=0 and solve for t:
h=-16t^+112t+6
0=-16t^+112t+6
applying the "quadratic formula" gives us:
x {-0.1, 7.1}
we can throw out the negative solution (extraneous) leaving
x = 7.1 seconds
.
Details of quadratic formula follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B112x%2B6+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28112%29%5E2-4%2A-16%2A6=12928.

Discriminant d=12928 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-112%2B-sqrt%28+12928+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28112%29%2Bsqrt%28+12928+%29%29%2F2%5C-16+=+-0.0531676008879738
x%5B2%5D+=+%28-%28112%29-sqrt%28+12928+%29%29%2F2%5C-16+=+7.05316760088797

Quadratic expression -16x%5E2%2B112x%2B6 can be factored:
-16x%5E2%2B112x%2B6+=+-16%28x--0.0531676008879738%29%2A%28x-7.05316760088797%29
Again, the answer is: -0.0531676008879738, 7.05316760088797. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B112%2Ax%2B6+%29