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1. You are given a quadratic function
y = - +
and they want you find its maximum.
For the general form quadratic function y = with the negative leading coefficient "a"
the maximum is achieved at x = -.
In your case a = , b = 1, so the maximum is achieved at
x = - = = 25 units.
To get the maximum value of the quadratic function, simply substitute x= 25 into the function
y = - = 12.5 units.
2. To find the horizontal distance traveled, simply find the distance between the roots (the zeroes) of the quadratic function:
y = 0 = - = .
The zeroes are x= 0 (where the cricket ball started his path) and x= 50 (where it is ended by hitting the ground).
The horizontal distance is 50 units.
Solved.
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On finding the maximum/minimum of a quadratic functions see 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
- OVERVIEW of lessons on finding the maximum/minimum of a quadratic function
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.