document.write( "Question 77495: I am having trouble finding the x-intercepts for the following situation.\r
\n" ); document.write( "\n" ); document.write( "The quarterback is standing on the opponents' 40-yard line. He throws a pass toward their goal line. The ball is 2 meters above the ground when the quarterback lets go. It follows a parabolic path, reaching its highest point, 14 meters above the ground, as it crosses the 20-yard line.
\n" ); document.write( "Can you Please help???? Thank you in advance. \n" ); document.write( "
Algebra.Com's Answer #55632 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
I am having trouble finding the x-intercepts for the following situation.
\n" ); document.write( "The quarterback is standing on the opponents' 40-yard line. He throws a pass toward their goal line. The ball is 2 meters above the ground when the quarterback lets go. It follows a parabolic path, reaching its highest point, 14 meters above the ground, as it crosses the 20-yard line.
\n" ); document.write( ":
\n" ); document.write( "How about this?
\n" ); document.write( "let the x = the yards from the point of throwing of the pass
\n" ); document.write( "The y = height of the football.
\n" ); document.write( ":
\n" ); document.write( "When the pass was thrown, x = 0 and y = 2; (also c = 2 in ax^2 + bx + c form)
\n" ); document.write( ":
\n" ); document.write( "At the highest point. x = 20 and y = 14
\n" ); document.write( ":
\n" ); document.write( "Since it is a parabola:
\n" ); document.write( "From y = 2 meters and the highest point is at 20 yds,
\n" ); document.write( " then at 40 yds, y will also = 2: so we have: x = 40; y = 2
\n" ); document.write( ":
\n" ); document.write( "Find a and b in the equation ax^2 + bx + c:
\n" ); document.write( ":
\n" ); document.write( "x = 20, y = 14
\n" ); document.write( "400a + 20b + 2 = 14
\n" ); document.write( "400a + 20b = 12; subtracted 2 from both sides:
\n" ); document.write( ":
\n" ); document.write( "x = 40, y = 2
\n" ); document.write( "1600a + 40b + 2 = 2
\n" ); document.write( "1600a + 40b = 0; subtracted 2 from both sides
\n" ); document.write( ":
\n" ); document.write( "Use the elimination method
\n" ); document.write( "Multiply the 1st equation by 4 and subtract from the 2nd equation to find b:
\n" ); document.write( "1600a + 40b = 0
\n" ); document.write( "1600a + 80b = 48
\n" ); document.write( "-------------------subtract
\n" ); document.write( "0 - 40b = -48
\n" ); document.write( "b = -48/-40
\n" ); document.write( "b = +1.2
\n" ); document.write( ":
\n" ); document.write( "Find a in 400a + 20b = 12, substitute 1.2 for b
\n" ); document.write( "400a + 20(1.2) = 12
\n" ); document.write( "400a + 24 = 12
\n" ); document.write( "400a = -12
\n" ); document.write( "400a = -12/400
\n" ); document.write( "a = -.03
\n" ); document.write( ":
\n" ); document.write( "Our equation would be: -.03x^2 + 1.2x + 2 = 0
\n" ); document.write( ":
\n" ); document.write( "A graph would look like this:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-10%2C+45%2C+-10%2C+25%2C+-.03x%5E2+%2B+1.2x+%2B+2%29+\"
\n" ); document.write( ":
\n" ); document.write( "The x intercept would be when it hit the ground in the end zone, (assuming no one caught it)
\n" ); document.write( ":
\n" ); document.write( "Find the x intercept using the quadratic formula a = -.03; b = 1.2; c = 2
\n" ); document.write( ":
\n" ); document.write( "You should get a positive solution of about 41.6 yds, or 1.6 yds into the end zone
\n" ); document.write( ":
\n" ); document.write( "Did this make sense to you? Thanks for an interesting problem. \n" ); document.write( "
\n" );