document.write( "Question 1014984: Hello, could you please help me with this word problem: In 1971, Apollo 14 astronaut Alan Shepard hit to golf balls on the moon. A golf enthusiasts of the future decides to play golf on many worlds throughout the solar system, and hits the golf ball consistently at an angle of 45° and a speed of 144 feet per second. The path of the golf ball can be modeled by the quadratic equation: y=- g/20736 x^2+x where X is the balls horizontal position (in feet) and G is its corresponding height (in feet) and she is the acceleration due to gravity (in feet per second squared).
\n" ); document.write( "What is the horizontal distance traveled by the golf ball on the moon, where G=5.32 and what is the maximum height of the golf ball on Mars, where G=12.17? \n" ); document.write( "
Algebra.Com's Answer #631361 by KMST(5328)\"\" \"About 
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The path of the golf ball can be modeled by the quadratic equation
\n" ); document.write( "\"y=-+gx%5E2%2F20736+%2Bx\" , where
\n" ); document.write( "\"x\" is the ball's horizontal position (in feet),
\n" ); document.write( "\"y\" is its corresponding height (in feet), and
\n" ); document.write( "\"g\" is the acceleration due to gravity (in \"feet%2Fsecond%5E2\" ).
\n" ); document.write( "
\n" ); document.write( "On the moon, \"g=5.32\" , so the ball is an the moon's surface, at \"y=0\" when
\n" ); document.write( "\"0=-5.32x%5E2%2F20736%2Bx\"-->\"0=%28-5.32%2F20736x-1%29x\"-->\"system%28x=0%2C%22or%22%2C-5.32%2F20736x=1%29\"-->\"system%28x=0%2C%22or%22%2Cx=20736%2F5.32=highlight%28about3898%29%29\"
\n" ); document.write( "There are two moments when the ball is on the moon's surface:
\n" ); document.write( "\"x=0\" (when the ball is hit and has not traveled horizontally), and
\n" ); document.write( "\"x=highlight%28about3898%29\" , when the ball hits the moon's surface after travelling a horizontal distance of about \"highlight%283898feet%29\"(rounded).
\n" ); document.write( "
\n" ); document.write( "When the golf ball is hit on Mars, where \"g=12.17\"\"feet%2Fsecond%5E2\" ,
\n" ); document.write( "the path of the golf ball can be modeled by the quadratic equation
\n" ); document.write( "\"y=-12.17x%5E2%2F20736+%2Bx\" , where
\n" ); document.write( "\"x\" is the ball's horizontal position (in feet), and
\n" ); document.write( "\"y\" is its corresponding height (in feet).
\n" ); document.write( "That equation represents a parabola
\n" ); document.write( "Your teacher wants you to remember that a quadratic function \"y=ax%5E2%2Bbx%2Bc\"
\n" ); document.write( "with \"a%3C0\"
\n" ); document.write( "represents a parabola with a vertex/maximum at
\n" ); document.write( "\"x=-b%2F2a\" ,
\n" ); document.write( "so you could apply that \"formula\" with \"a=-12.17%2F20736\" and \"b=1\" ,
\n" ); document.write( "and then you could substitute the \"x=about852\" value found into \"y=-12.17x%5E2%2F20736+%2Bx\" to find the maximum height,
\n" ); document.write( "\"y=-12.17%2A852%5E2%2F20736%2B852=about426\".
\n" ); document.write( "Alternately, you could \"complete the square\":
\n" ); document.write( "\"y=-12.17x%5E2%2F20736+%2Bx\"
\n" ); document.write( "\"%28-20736%2F12.17%29y=x%5E2%2B%28-20736%2F12.17%29x\"
\n" ); document.write( "
\n" ); document.write( "\"%28-20736%2F12.17%29y%2B20736%5E2%2F%284%2A12.17%5E2%29=%28x-20736%2F%282%2A12.17%29%29%5E2\"
\n" ); document.write( "\"%28-20736%2F12.17%29%28y-20736%2F%284%2A12.17%29%29=%28x-20736%2F%282%2A12.17%29%29%5E2\"
\n" ); document.write( "So, \"%28-20736%2F12.17%29%28y-20736%2F%284%2A12.17%29%29%3E=0\"-->\"y-20736%2F%284%2A12.17%29%3C=0\"-->\"y%3C=20736%2F%284%2A12.17%29=about426\"} .
\n" ); document.write( "So, in Mars, the ball reaches a height of \"highlight%28426feet%29\" . \n" ); document.write( "
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