\r\n" );
document.write( "y = -x^2+3x-4\r\n" );
document.write( "\r\n" );
document.write( "compare to:\r\n" );
document.write( "\r\n" );
document.write( "y = ax^2+bx+c\r\n" );
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document.write( "a=-1, b=3, c=-4\r\n" );
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document.write( "1. It has an x^2 term, so the graph of the equation is a parabola.\r\n" );
document.write( "2. The coefficient of the x^2 term, a=-1, is negative so the parabola opens downward.\r\n" );
document.write( "3. The constant term c is -4, so the y-intercept is (0,c) = (0,-4).\r\n" );
document.write( "4. To find the vertex we use the vertex formula for the x-coordinate of the vertex,\r\n" );
document.write( "which is 
, that also tells us that the line of symmetry \r\n" );
document.write( "has equation 
\r\n" );
document.write( "5. The y-coordinate of the vertex is found by substituting the x-coordinate\r\n" );
document.write( "of the vertex, h, for x in the original equation:\r\n" );
document.write( "
\r\n" );
document.write( "6. The vertex is below the x-axis and the parabola opens downward so there\r\n" );
document.write( "are no x-intercepts, and there is no use to try to find any.\r\n" );
document.write( "7. The vertex is the point (h,k) = 
\r\n" );
document.write( "8. We plot the vertex, the y-axis and the line of symmetry (in green):\r\n" );
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document.write( "
\r\n" );
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document.write( "9. Using the line of symmetry, we find the point symmetrical to the y-intercept,\r\n" );
document.write( "which is (3,-4) on the other side of the line of symmetry:\r\n" );
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document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "10. And now it's easy to sketch in the parabola:\r\n" );
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document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
