document.write( "Question 177929: A baseball is hit and follows a parabolic path described by the function y=-3x^2+18x+1, where x represents the time in seconds after the ball is hit and y represents the ball's height in meters from the ground. Algebraically determine the maximum height and the time at which the ball reaches its maximum height. \n" ); document.write( "
Algebra.Com's Answer #132950 by nerdybill(7384)\"\" \"About 
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By inspecting:
\n" ); document.write( "y=-3x^2+18x+1
\n" ); document.write( "We see that the first coefficient is -3, this means it's a parabola in the shape of an \"upside down U\". This means, if we find the \"vertex\" of the parabola, it will be at the peak of the parabola.
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\n" ); document.write( "The idea is to \"complete the square\" to get it into the \"standard vertex\" form:
\n" ); document.write( "y= a(x-h)^2+k
\n" ); document.write( "where (h,k) is the maximum.
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\n" ); document.write( "y=-3x^2+18x+1
\n" ); document.write( "y=(-3x^2+18x)+1
\n" ); document.write( "y=-3(x^2-6x)+1
\n" ); document.write( "y=-3(x^2-6x+9)+1+27
\n" ); document.write( "y=-3(x-3)(x-3)+28
\n" ); document.write( "y=-3(x-3)^2+28
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\n" ); document.write( "Therefore,
\n" ); document.write( "(h,k)= (3,28)
\n" ); document.write( "This says, that at 3 seconds the ball is at the peak of 28 meters.\r
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