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The height of the ball over the ground is described by a quadratic function
h(t) = - 16*t^2 + 32t + 20. (1)
The maximum height is achieved when the quadratic function (1) has the maximum.
From algebra, the quadratic function y = ax^2 + bx + x has extremum at x = .
In your case, a= -16, b= 32, so x= = 1.
Thus the quadratic function (1) achieved maximum at t = 1. It means that the ball will achieve the maximum height at t= 1 seconds.
And the maximum height will be h(1) = -16*1^2 + 32*1 + 20 = 36 ft.
Answer. The ball will achieve its maximum height of 36 ft in 1 second.
Solved.
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On finding the maximum/minimum of a quadratic function see the lessons in this site
- 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
- OVERVIEW of lessons on finding the maximum/minimum of a quadratic function
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.