Question 1126066
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<pre>
1.  You are given a quadratic function

       y = -{{{x^2/50}}} + {{{x}}}

    and they want you find its maximum.



        For the general form quadratic function  y = {{{ax^2 + bx + c}}}  with the negative leading coefficient  "a"  
        the maximum is achieved at  x = -{{{b/(2a)}}}.


    In your case  a = {{{-1/50}}},  b = 1,  so the maximum is achieved at  

       x = -{{{1/((-2/50)) }}} = {{{50/2}}} = 25 units.


    To get the maximum value of the quadratic function, simply substitute x= 25 into the function

       y = {{{25}}} - {{{25^2/50}}} = 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 = {{{x}}} - {{{x^2/50}}} = {{{x*(1-x/50)}}}.


    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.
</pre>

Solved.


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On finding the maximum/minimum of a quadratic functions see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/OVERVIEW-of-lessons-on-finding-the-maximum-minimum-of-a-quadratic-function.lesson>OVERVIEW of lessons on finding the maximum/minimum of a quadratic function</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Finding minimum/maximum of quadratic functions</U>". 



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.