document.write( "Question 499336: how do i sketch f(x)=x squared - 5x-6
\n" ); document.write( "how do i give an equation for the line of symmetry of the graph. how do i estimate the cordinates if the lowest point on the graph \n" ); document.write( "

Algebra.Com's Answer #337590 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=x%5E2+-5x-6\"$ or $\"y=x%5E2+-5x-6\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The general form of a quadratic is \" $\"y+=+ax%5E2+%2B+bx+%2B+c\"$ \". \r
\n" ); document.write( "\n" ); document.write( "For graphing, the leading coefficient \" $\"a\"$ \" indicates how \" $\"fat\"$ \" or how \" $\"skinny\"$ \" the $\"parabola\"$ will be.\r
\n" ); document.write( "\n" ); document.write( "For |a| > $\"1\"$ (such as $\"a+=+3\"$ or $\"a+=+-4\"$ ), the parabola will be \" $\"skinny\"$ \", because it $\"grows\"$ more $\"quickly\"$ (three times as fast or four times as fast, respectively, in the case of our sample values of a). \r
\n" ); document.write( "\n" ); document.write( "For | a | < $\"1\"$ (such as $\"a+=+1%2F3\"$ or $\"a+=+-1%2F4\"$ ), the parabola will be \" $\"fat\"$ \", because it $\"grows\"$ more $\"slowly\"$ (one-third as fast or one-fourth as fast, respectively, in the examples). \r
\n" ); document.write( "\n" ); document.write( "Also, if $\"a\"$ is $\"negative\"$ , then the parabola is $\"upside-down\"$ .\r
\n" ); document.write( "\n" ); document.write( "In your case, $\"a\"$ is $\"positive\"$ and the parabola is $\"upward\"$ .\r
\n" ); document.write( "\n" ); document.write( "If the quadratic is written in the form $\"y=a%28x-h%29%5E2%2Bk\"$ (the vertex form), then the vertex is the point ( $\"h\"$ , $\"k\"$ ). \r
\n" ); document.write( "\n" ); document.write( "For a given quadratic $\"y+=+ax%5E2+%2B+bx+%2B+c\"$ , the vertex ( $\"h\"$ , $\"k\"$ ) is found by computing $\"h=-b%2F2a\"$ , and $\"k=%284ac-b%5E2%29%2F4a\"$ .\r
\n" ); document.write( "\n" ); document.write( "In your case, $\"y=x%5E2+-5x-6\"$ , the vertex ( $\"h\"$ , $\"k\"$ ) will be:\r
\n" ); document.write( "\n" ); document.write( " $\"h=-b%2F2a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h=-%28-5%29%2F2%2A1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h+=5%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"h+=2.5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k=%284ac-b%5E2%29%2F4a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k=%284%2A1%2A%28-6%29-%28-5%29%5E2%29%2F4%2A1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k=%28-24-25%29%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k+=-49+%2F+4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"k+=-12.25\"$ \r
\n" ); document.write( "\n" ); document.write( "so, \r
\n" ); document.write( "\n" ); document.write( "the vertex ( $\"h\"$ , $\"+k\"$ ) is at ( $\"2.5\"$ , $\"-12.25\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the \" $\"axis\"$ of $\"symmetry\"$ \"\r
\n" ); document.write( "\n" ); document.write( "If you look at a parabola, you'll notice that you could $\"draw\"$ a $\"vertical\"$ line right up through the middle which would split the parabola into two mirrored halves. This vertical line, right $\"through\"$ the $\"vertex\"$ , is called the $\"axis\"$ of $\"symmetry\"$ . \r
\n" ); document.write( "\n" ); document.write( "If you're asked for the axis, write down the line \" $\"x+=+h\"$ \", where $\"h\"$ is just the $\"x-coordinate\"$ of the vertex. So in the example above, then the axis would be the vertical line $\"x+=+h+=+2.5\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-15%2C+10%2C+x%5E2+-5x-6%29+\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );