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You can put this solution on YOUR website!
rightio..i understand now :-)\r
\n" ); document.write( "\n" ); document.write( "however, the point (-1, 2) is not an intercept, it is the maximum (or minimum) point on the curve...\r
\n" ); document.write( "\n" ); document.write( "ok. where an equation/line/curve crosses the x-axis is where y=0. Finding such values (called the roots of the equation) is the main aim in algebra like this.\r
\n" ); document.write( "\n" ); document.write( "typically we have a quadratic equation equal to zero which we factorise because then we have 2 parts that multiply to equal zero. For this to be true, one of those 2 parts must be zero itself. Which one? either.\r
\n" ); document.write( "\n" ); document.write( "so here, we work backwards...we know that the roots are x=1 and x=-3, so we know that\r
\n" ); document.write( "\n" ); document.write( "(x-1)(x+3) = 0
\n" ); document.write( "so, now we can multiply this out to give
\n" ); document.write( "\n" ); document.write( "so what is the equation? well it is
\n" ); document.write( "\n" ); document.write( "So we have 2 quadratics that both go through the 2 roots mentioned. Here they are sketched...\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As you can see, they are both symmetric about the max/min axis (at x=-1). So we need this third point to tell us which of the 2 curves, and hence, which of the 2 equations we had.\r
\n" ); document.write( "\n" ); document.write( "Note:
\n" ); document.write( "a u-shape quadratic has +ve x-squared term
\n" ); document.write( "a n-shape quadratic has -ve x-squared term\r
\n" ); document.write( "\n" ); document.write( "so, the point (-1, 2) should lie on the n-shaped curve and hence our equation was
\n" ); document.write( "\n" ); document.write( "Hope this was of help to you.\r
\n" ); document.write( "\n" ); document.write( "cheers
\n" ); document.write( "Jon. \n" ); document.write( "