document.write( "Question 812303: John owns a hot dog stand. He has found that his profit is represented by the equation P(x) = [ (-1)x^2 + 62x + 77 ],
\n" ); document.write( "with P being profits and x the number of hot dogs sold. How many hot dogs must he sell to earn the most
\n" ); document.write( "profit? \n" ); document.write( "
Algebra.Com's Answer #489089 by TimothyLamb(4379)\"\" \"About 
You can put this solution on YOUR website!
y = (-1)x^2 + 62x + 77
\n" ); document.write( "---
\n" ); document.write( "---
\n" ); document.write( "the above quadratic equation is in standard form, with a=-1, b=62, and c=77
\n" ); document.write( "---
\n" ); document.write( "the x coordinate of the max (or min) of the quadratic function is given by: x = -b/2a
\n" ); document.write( "---
\n" ); document.write( "x = -b/2a
\n" ); document.write( "x = -62/2(-1)
\n" ); document.write( "---
\n" ); document.write( "x = 31
\n" ); document.write( "---
\n" ); document.write( "the y coordinate of the max (or min) of the quadratic function is found by evaluating the function at the x coordinate of the max (or min)
\n" ); document.write( "---
\n" ); document.write( "y = (-1)x^2 + 62x + 77
\n" ); document.write( "y = -(31^2) + 62(31) + 77
\n" ); document.write( "y = -(31^2) + 62(31) + 77
\n" ); document.write( "y = 1038
\n" ); document.write( "---
\n" ); document.write( "because a < 0 the vertex of the quadratic is a maximum, and (31, 1038) is the maximum.
\n" ); document.write( "---
\n" ); document.write( "Answer:
\n" ); document.write( "he must sell 31 to earn the maximum profit of 1038
\n" ); document.write( "---
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-60%2C+120%2C+-100%2C+1200%2C+-x%5E2+%2B+62x+%2B+77%29+\"
\n" ); document.write( "---
\n" ); document.write( "Solve and graph linear equations:
\n" ); document.write( "https://sooeet.com/math/linear-equation-solver.php
\n" ); document.write( "---
\n" ); document.write( "Solve quadratic equations, quadratic formula:
\n" ); document.write( "https://sooeet.com/math/quadratic-formula-solver.php
\n" ); document.write( "---
\n" ); document.write( "Convert fractions, decimals, and percents:
\n" ); document.write( "https://sooeet.com/math/fraction-decimal-percent.php
\n" ); document.write( "---
\n" ); document.write( "Calculate and graph the linear regression of any data set:
\n" ); document.write( "https://sooeet.com/math/linear-regression.php \n" ); document.write( "
\n" );