document.write( "Question 316882: I neeed help graphing f(x)=x^2-7x-8 I need to understand how to find the vertex, x-intercept,line of symmetry, and the opening of the graph. \n" ); document.write( "
Algebra.Com's Answer #226816 by texttutoring(324)![]() ![]() You can put this solution on YOUR website! y = x^2-7x-8\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "To find the x intercepts, simply set y=0 and solve for x (by factoring): \n" ); document.write( "0=x^2-7x-8 \n" ); document.write( "0=(x-8)(x+1)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The x-intercepts are x=8 and x= -1.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The easiest way to graph it is to complete the square, to turn it into a form that is more easily graphed:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Completing the square:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "y = x^2-7x-8 (halve the b term, -7, and then square it: (-7/2)^2 = 49/4)\r \n" ); document.write( "\n" ); document.write( "y = x^2 -7x +49/4 - 8 - 49/4 (add 49/4 beside the b term, -7, but then subtract it after the -8 term)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "y = (x - 7/2)^2 - 8 - 49/4 \n" ); document.write( "y = (x - 7/2)^2 - 81/4\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So the vertex is at (7/2, -81/4)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "It opens up (because the x^2 term is positive), and the line of symmetry is just the x-coordinate of the vertex, 7/2.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Hope that helps. Let me know if you're still stuck! \n" ); document.write( " |