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They want you find the maximum of the quadratic function h(t) = -16*t^2 + 46t + 4 as the function of variable "t".
For any quadratic function of the general form f(x) = ax^2 + bx + c with negative coefficient "a", its maximum is achieved at x = .
In your case a = -16, b= 46. Hence, the given function h(t) achieves the maximum at t = = = seconds.
To find the maximum value of h(t), substitute this value t= into the formula for h(t) and calculate
= = = 37.06 ft (approximately).
Answer. The maximum height is 37.06 ft (approximately, with two valid decimal places after the decimal point).
Solved.
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On finding the maximum/minimum of a quadratic function see my 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.
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.
To see many other similar solved problems on a projectile thrown/shot/launched vertically up, look 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.
The referred lessons are the part of the same textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".