document.write( "Question 825613: If x=3 is the equation of the axis of symmetry of the graph of y=x^2-6x+10 what is the y coordinate of the turning point ? \n" ); document.write( "

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A standard quadratic equation like y = x^2 is a U-shaped curve that is centred on the origin, has its axis of symmetry as the line x = 0, and has its turning point at the origin also, i.e. where y = 0.
\n" ); document.write( "If we translate this graph about the x-y plane such that its origin is now at the coords (h,k), then the new equation of the curve is,
\n" ); document.write( "(y-k) = (x-h)^2
\n" ); document.write( "And here the axis of symmetry is the line x = h and the bottom of the curve (its turning point) is on the line y = k.
\n" ); document.write( "Our graph is y = x^2 - 6x + 10
\n" ); document.write( "completing the square on the rhs gives us,
\n" ); document.write( "y = x^2 - 6x + 9 + 1
\n" ); document.write( "y = (x - 3)^2 + 1
\n" ); document.write( "(y - 1) = (x - 3)^2
\n" ); document.write( "Here (h,k) = (3,1).
\n" ); document.write( "So the origin of this curve is the point (x,y) = (3,1).
\n" ); document.write( "Thus the y-coordinate of its turning point is y = 1. \n" ); document.write( "

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