document.write( "Question 1126066: The equation of the path of a cricket ball thrown is y = x - (x^2/50), where x m and y m are the horizontal and vertical heights, travelled respectively. Calculate the greatest vertical height reached and the horizontal distance travelled. \n" ); document.write( "

Algebra.Com's Answer #742471 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "1.  You are given a quadratic function\r\n" );
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document.write( "       y = - + \r\n" );
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document.write( "    and they want you find its maximum.\r\n" );
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document.write( "        For the general form quadratic function  y =   with the negative leading coefficient  \"a\"  \r\n" );
document.write( "        the maximum is achieved at  x = -.\r\n" );
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document.write( "    In your case  a = ,  b = 1,  so the maximum is achieved at  \r\n" );
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document.write( "       x = - =  = 25 units.\r\n" );
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document.write( "    To get the maximum value of the quadratic function, simply substitute x= 25 into the function\r\n" );
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document.write( "       y =  -  = 12.5 units.\r\n" );
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document.write( "2.  To find the horizontal distance traveled, simply find the distance between the roots (the zeroes) of the quadratic function:\r\n" );
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document.write( "        y = 0 =  -  = .\r\n" );
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document.write( "    The zeroes are  x= 0  (where the cricket ball started his path)  and  x= 50 (where it is ended by hitting the ground).\r\n" );
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document.write( "    The horizontal distance is 50 units.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic functions see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on finding the maximum/minimum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Finding minimum/maximum of quadratic functions\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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