document.write( "Question 1102316: If a baseball that is hit follows a parabolic path 72 meters at the base and 16 meters high at the center,find the equation of a parabola that gives the path of the baseball. Note that the departure of the ball is point of origin. \n" ); document.write( "

Algebra.Com's Answer #716979 by htmentor(1343) $\"\"$ $\"About$

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First let's assume the path is symmetric about y-axis.
\n" ); document.write( "Then we can shift the parabola along the x-axis to make the departure point the origin.
\n" ); document.write( "The equation will take on the form y = ax^2 + c. The vertex will be at the point
\n" ); document.write( "(0,16), and the endpoints of the base are (-36,0) and (36,0)
\n" ); document.write( "Thus 16 = a*0 + c -> c = 16
\n" ); document.write( "Use one of the base points to find a
\n" ); document.write( "0 = a*36^2 + 16 -> a = -16/36^2 = -1/81
\n" ); document.write( "In order to have the parabola start at the origin, we make a translation along the x-axis:
\n" ); document.write( "x -> x-36
\n" ); document.write( "The final equation is y = (-1/81)(x-36)^2 + 16
\n" ); document.write( "Note that the leading coefficient, a, is equal to -h/(b/2)^2, where h is the height and b is the base \n" ); document.write( "

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