document.write( "Question 211525: from the center of the 20yd (60ft) line, a football player attempts to make a field goal by kicking the ball directly toward the goal posts, which are 90ft away. The goal-post crossbar is 10 ft above the ground. The ball reaches its highest altitude of 32 ft at a point 48 ft from where it was kicked.
\n" ); document.write( "a. make a sketch showing the path of the football. if the point from which the ball is kicked is the origin of a coordinate plane, find the equation of the parabolic path of the football.
\n" ); document.write( "b. will the kicker make the field goal?
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Algebra.Com's Answer #159870 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The football is kicked at point (0,0).\r\n" );
document.write( "The highest point (vertex) is at (48,32)\r\n" );
document.write( "The goalpost crossbar is at (90,10).\r\n" );
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document.write( "We begin by plotting the vertex, and drawing\r\n" );
document.write( "a line for the goalpost.\r\n" );
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document.write( "The equation of a parabola is\r\n" );
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document.write( "\"y=a%28x-h%29%5E2%2Bk\" where the vertex is \"%22%28h%2Ck%29%22\"\r\n" );
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document.write( "We substitute \"%22%28h%2Ck%29%22=%22%2848%2C32%29%22\"\r\n" );
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document.write( "\"y=a%28x-48%29%5E2%2B32\"\r\n" );
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document.write( "We can find \"a\" because the parabola goes\r\n" );
document.write( "through the origin \"%22%280%2C0%29%22\"\r\n" );
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document.write( "So we substitute \"%22%28x%2Cy%29%22=%22%280%2C0%29%22\"\r\n" );
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document.write( "\"y=a%28x-48%29%5E2%2B32\"\r\n" );
document.write( "\"0=a%280-48%29%5E2%2B32\"\r\n" );
document.write( "\"0=a%28-48%29%5E2%2B32\"\r\n" );
document.write( "\"0=a%282304%29%2B32\"\r\n" );
document.write( "\"0=2304a%2B32\"\r\n" );
document.write( "\"-32=2304a\"\r\n" );
document.write( "\"%28-32%2F2304%29=a\"\r\n" );
document.write( "\"-1%2F72=a\"\r\n" );
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document.write( "So the equation of the parabola is\r\n" );
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document.write( "\"y=%28-1%2F72%29%28x-48%29%5E2%2B32\"\r\n" );
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document.write( "We draw the parabola:\r\n" );
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document.write( "Oh,oh.  From the picture it appears that the\r\n" );
document.write( "football is going to drop too low to go over\r\n" );
document.write( "the goal post bar.  But we can't just go by the \r\n" );
document.write( "picture.  Let's calculate the height of the \r\n" );
document.write( "ball when \"x=90\" and find out for sure:\r\n" );
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document.write( "\"y=%28-1%2F72%29%28x-48%29%5E2%2B32\"\r\n" );
document.write( "\"y=%28-1%2F72%29%2890-48%29%5E2%2B32\"\r\n" );
document.write( "\"y=%28-1%2F72%29%2842%29%5E2%2B32\"\r\n" );
document.write( "\"y=%28-1%2F72%29%281764%29%2B32\"\r\n" );
document.write( "\"y=%28-1764%2F72%29%2B32\"\r\n" );
document.write( "\"y=-24.5%2B32\"\r\n" );
document.write( "\"y=7.5\"\r\n" );
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document.write( "No, the field goal will not be made, because\r\n" );
document.write( "the ball will be too low, and will go under\r\n" );
document.write( "the goal post, since 7.5 feet is less\r\n" );
document.write( "than 10 feet.\r\n" );
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document.write( "Edwin
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