document.write( "Question 833799: suppose a parabola has an axis of symmetry at x=1, a maximum height of 6 and also through the point (2,4). write the equation of the parabola in vertex form \n" ); document.write( "
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suppose a parabola has an axis of symmetry at x=1, a maximum height of 6 and also through the point (2,4). write the equation of the parabola in vertex form
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\n" ); document.write( "Vertex form of a parabola is:
\n" ); document.write( "y = a(x-h)^2 + k
\n" ); document.write( "where
\n" ); document.write( "(h,k) is the vertex
\n" ); document.write( ".
\n" ); document.write( "Since the \"axis of symmetry is at x=1\"
\n" ); document.write( "the 'h' value must be 1
\n" ); document.write( "since the max height is at 6
\n" ); document.write( "the 'k' value must be 6
\n" ); document.write( "so, now we have
\n" ); document.write( "y = a(x-1)^2 + 6
\n" ); document.write( ".
\n" ); document.write( "to find 'a', plug in (2,4) and solve for 'a':
\n" ); document.write( "y = a(x-1)^2 + 6
\n" ); document.write( "4 = a(2-1)^2 + 6
\n" ); document.write( "4 = a(1)^2 + 6
\n" ); document.write( "-2 = a(1)
\n" ); document.write( "-2 = a
\n" ); document.write( ".
\n" ); document.write( "answer:
\n" ); document.write( "y = -2(x-1)^2 + 6
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