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A football is thrown upward from a height of 6 feet with an initial velocity of 65 feet per second.
Let t= the time in seconds after the football is thrown.
Let h= the height of the football. The quadratic function h(t)=-16t^2+65t+6 represents
the height of the football as a function of time.
Use technology to deter sun the absolute maximum of the function and interpret
what absolute maximum means in terms of the scenario.
The absolute maximum of the function is..?
The absolute maximum of the function means that..?
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The function s(t) = -16t^2 + 65t + 6 is a quadratic function, whose plot is a parabola opened down.
This quadratic function has the maximum at the value of its argument t = , where
"a" is the coefficient at t^2 and "b" is the coefficient at t.
In your case, a= -16, b= 65, so the function gets the maximum at t = = 2.03125 seconds.
So, the ball gets the maximum height 2.03125 seconds after is hit straight up.
The maximum height is then s(2.03125) = -16*2.03125^2 + 65*2.03125 + 6 = 72.01563 feet. ANSWER
Solved.
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To see many other similar solved problems, slook into the lessons
- Problem on a projectile moving vertically up and down
- Problem on an arrow shot vertically upward
- Problem on a ball thrown vertically up from the top of a tower
- Problem on a toy rocket launched vertically up from a tall platform
in this site.
On finding the maximum/minimum of a quadratic function, learn from the lessons
- HOW TO complete the square to find the minimum/maximum of a quadratic function
- Briefly on finding the minimum/maximum of a quadratic function
- HOW TO complete the square to find the vertex of a parabola
- Briefly on finding the vertex of a parabola
in this site.