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When a gray kangaroo jumps, its path through the air can be modeled by:
\n" ); document.write( " y = -0.0267x2 + 0.8x where x is the kangaroo's horizontal distance traveled (in feet) wand y is the corresponding height (in feet).
\n" ); document.write( " How high can a gray kangaroo jump?
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\n" ); document.write( "y = -0.0267x^2 + 0.8x
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\n" ); document.write( "Find the max height by finding the axis of symmetry; Formula: x = -b/(2a)
\n" ); document.write( "In this equation: a = -.0267; b = .8, so we have:
\n" ); document.write( "x =
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\n" ); document.write( "x =
\n" ); document.write( "x = +14.98; max height occurs at horizontal dist of 14.98 ft
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\n" ); document.write( "Find the max height, replace x with 14.98 in the original equation
\n" ); document.write( "y = -0.0267(14.98^2) + 0.8(14.98)
\n" ); document.write( "y = -0.026y(224.4) + 11.984
\n" ); document.write( "y = -5.99 + 11.984
\n" ); document.write( "y ~ 6 ft is max height
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\n" ); document.write( "How far can it jump? When this occurs, y = 0
\n" ); document.write( "-0.0267x^2 + 0.8x = 0
\n" ); document.write( "Factor out -x
\n" ); document.write( "x(.0267x - 0.8) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = 0; the starting point of the leap
\n" ); document.write( "and
\n" ); document.write( ".0267x = +.8
\n" ); document.write( "x =
\n" ); document.write( "x = 29.96 ~ 30 ft is the distance he can jump (landing point)
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\n" ); document.write( "Would look like this graphically
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