document.write( "Question 166632: An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and the f(x) is the vertical distance the football travels. The bottom of the uprights is 3.5 yards above the ground.\r
\n" ); document.write( "\n" ); document.write( "1. Assuming the kick is in between the uprights, did the kicker make the field goal? Why or Why not?\r
\n" ); document.write( "\n" ); document.write( "2. Would the kicker have made a 42-yard field goal with the same kick? Why or Why not? \n" ); document.write( "
Algebra.Com's Answer #122812 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and f(x) is the vertical distance the football travels. The bottom of the upright is 3.5 yards above the ground.
\n" ); document.write( "Assuming the kick is in between the uprights, did the kicker make the field goal? Why or Why not?
\n" ); document.write( ":
\n" ); document.write( "Find value of (x) (dist) when f(x) = 3.5 (height)
\n" ); document.write( "-.0625x² + 2.7x = 3.5
\n" ); document.write( ":
\n" ); document.write( "-.0625x² + 2.7x - 3.5 = 0
\n" ); document.write( ":
\n" ); document.write( "Use the quadratic formula:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "In this problem a=-.0625; b=+2.7; c=-3.5
\n" ); document.write( "\"x+=+%28-2.7+%2B-+sqrt%282.7%5E2+-+4+%2A+-.0625+%2A+-3.5+%29%29%2F%282%2A-.0625%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%28-2.7+%2B-+sqrt%287.29+-+.875%29%29%2F%28-.125%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%28-2.7+%2B-+sqrt%286.415%29%29%2F%28-.125%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%28-2.7+%2B+2.533%29%2F%28-.125%29+\"
\n" ); document.write( "\"x+=+%28-.167%29%2F%28-.125%29+\"
\n" ); document.write( "x = 1.33; not the solution we want here
\n" ); document.write( "and
\n" ); document.write( "\"x+=+%28-2.7+-+2.533%29%2F%28-.125%29+\"
\n" ); document.write( "\"x+=+%28-5.233%29%2F%28-.125%29+\"
\n" ); document.write( "x = 41.86 yds; clears the upright nicely
\n" ); document.write( ":
\n" ); document.write( "The ball had traveled almost 42 yds when it had descended to 3.5 meters
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "2. Would the kicker have made a 42-yard field goal with the same kick? Why or Why not?.
\n" ); document.write( "Find the height at 42 yds
\n" ); document.write( "h = -.0625x² + 2.7x
\n" ); document.write( "Substitute 42 for x
\n" ); document.write( "h = -.0625(42^2) + 2.7(42)
\n" ); document.write( "h = -.0625(1764) + 113.4
\n" ); document.write( "h = -110.25 + 113.4
\n" ); document.write( "h = 3.15 yds, So No; just under the bar at 3.5 yds high\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );