document.write( "Question 1157025: Please help me list the directions,vertex, axis of symmetry, table of 5 points, graph ?
\n" ); document.write( "1.F(x)= (x-6)^2+2\r
\n" ); document.write( "\n" ); document.write( "2. F(x) = x^2-2x-5 \n" ); document.write( "

Algebra.Com's Answer #779814 by MathLover1(20849) $\"\"$ $\"About$

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graphing the following and listing the directions,vertex,axis of symmetry,table with $\"5\"$ points and the graph for this equation\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-6%29%5E2%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( "from given formula you see that $\"h=6\"$ and $\"k=2\"$ , so vertex is at ( $\"6\"$ , $\"2\"$ )\r
\n" ); document.write( "\n" ); document.write( "so, we have one point for a graph\r
\n" ); document.write( "\n" ); document.write( "For a parabola in standard form: $\"y=ax%5E2%2Bbx%2Bc\"$
\n" ); document.write( "the axis of symmetry is the $\"vertical\"$ line that goes through the vertex
\n" ); document.write( " $\"x=+-b%2F2a\"$ \r
\n" ); document.write( "\n" ); document.write( "in your case, $\"x\"$ coordinate of the vertex is $\"6\"$ =:the $\"vertical\"$ line that goes through the vertex
\n" ); document.write( " $\"x=+6\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "directrix:\r
\n" ); document.write( "\n" ); document.write( " $\"4p+%28y-k+%29=+%28x-h+%29%5E2\"$ is the standard equation for an up-down facing parabola with vertex at ( $\"h\"$ , $\"k+\"$ ) and a focal length $\"+abs%28p%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Rewrite $\"y=+%28x-6+%29%5E2%2B2\"$ in the standard form:
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\n" ); document.write( " $\"4p%28y-2+%29=+%28x-6+%29%5E2\"$ .....since $\"4p=1\"$ => $\"p=1%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=2-p\"$
\n" ); document.write( " $\"y=2-1%2F4\"$
\n" ); document.write( " $\"y=8%2F4-1%2F4\"$
\n" ); document.write( " $\"y=7%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( "table:\r
\n" ); document.write( "\n" ); document.write( " $\"x\"$ | $\"y\"$
\n" ); document.write( " $\"6\"$ | $\"2\"$
\n" ); document.write( " $\"5\"$ | $\"3\"$
\n" ); document.write( " $\"4\"$ | $\"6\"$
\n" ); document.write( " $\"7\"$ | $\"3\"$
\n" ); document.write( " $\"8\"$ | $\"6\"$ \r
\n" ); document.write( "\n" ); document.write( "

\r
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\n" ); document.write( "\n" ); document.write( "2.
\n" ); document.write( " $\"F%28x%29+=+x%5E2-2x-5\"$ .....write in vertex form\r
\n" ); document.write( "\n" ); document.write( " $\"F%28x%29+=+%28x%5E2-2x%2Bb%5E2%29-b%5E2-5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"F%28x%29+=+%28x%5E2-2x%2B1%5E2%29-1%5E2-5\"$
\n" ); document.write( " $\"F%28x%29+=+%28x-1%29%5E2-6\"$ \r
\n" ); document.write( "\n" ); document.write( "vertex | ( $\"1\"$ , $\"-6\"$ )\r
\n" ); document.write( "\n" ); document.write( "compare to $\"4p+%28y-k+%29=+%28x-h+%29%5E2\"$ => $\"4p=1\"$ => $\"p=1%2F4\"$
\n" ); document.write( " $\"y=-6-p\"$
\n" ); document.write( " $\"y=-6-1%2F4\"$
\n" ); document.write( " $\"y=-25%2F4\"$
\n" ); document.write( "directrix: $\"y+=+-25%2F4\"$ \r
\n" ); document.write( "\n" ); document.write( "axis of symetry:the $\"vertical\"$ line that goes through the vertex
\n" ); document.write( " $\"x=+1\"$ \r
\n" ); document.write( "\n" ); document.write( "table:\r
\n" ); document.write( "\n" ); document.write( " $\"x\"$ | $\"y\"$
\n" ); document.write( " $\"1\"$ | $\"-6\"$
\n" ); document.write( " $\"2\"$ | $\"-5\"$
\n" ); document.write( " $\"3\"$ | $\"-2\"$
\n" ); document.write( " $\"4\"$ | $\"3\"$
\n" ); document.write( " $\"0\"$ | $\"-5\"$ \r
\n" ); document.write( "\n" ); document.write( "

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