document.write( "Question 122464: A skier decides to jump a ramp. The path of the jump can be represented by the quadratic relationship h(t)=-6t^2+12t+1 where h represents the height above the ground in metres, and t represents time after leaving the ramp in seconds. Algebraically determine the maximum height reached by the jumper and the time at which this maximum height occurs. \n" ); document.write( "

Algebra.Com's Answer #89986 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A skier decides to jump a ramp. The path of the jump can be represented by the quadratic relationship h(t)=-6t^2+12t+1 where h represents the height above the ground in meters, and t represents time after leaving the ramp in seconds.
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\n" ); document.write( " Algebraically determine the maximum height reached by the jumper and the time at which this maximum height occurs.
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\n" ); document.write( "The maximum height will occur at the axis of symmetry which can be found using
\n" ); document.write( "x = -b/(2a); in this equation: a=-6; b=12
\n" ); document.write( ":
\n" ); document.write( "t = $\"%28-12%29%2F%282%2A-6%29\"$
\n" ); document.write( "t = $\"%28-12%29%2F%28-12%29\"$
\n" ); document.write( "t = 1 sec
\n" ); document.write( ":
\n" ); document.write( "Find the vertex (max height); substitute 1 for t in the original equation
\n" ); document.write( "h(t) = -6(1^2) + 12(1) + 1
\n" ); document.write( "h(t) = -6 + 12 + 1
\n" ); document.write( "h(t) = +7 meters \n" ); document.write( "

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