document.write( "Question 103593: Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).\r
\n" ); document.write( "\n" ); document.write( "y = –x^2 + 3x – 3
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Algebra.Com's Answer #75326 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
there is no \"x\" intercept
\n" ); document.write( "\"y\" intercept is \"-3.0\" (if \"x=0\" => \"y=-3\")
\n" ); document.write( "\"x1\" and \"x2\" have a real and imaginary part
\n" ); document.write( "\"x2\"=\"1.5\" +\".866i\"\"+i\"
\n" ); document.write( "\"x2\"=\"1.5\" - \".866i\"\"+i\"\r
\n" ); document.write( "\n" ); document.write( "\"vertex%28h%2Ck%29\"
\n" ); document.write( "\"h=-b%2F2a\"
\n" ); document.write( "\"h=-3%2F2%2A%28-1%29\"
\n" ); document.write( "\"h=3%2F2=1.5\"
\n" ); document.write( "\"k=+y%28h%29\"
\n" ); document.write( "\"k=-1%2A%283%2F2%29%5E2+%2B3%283%2F2%29+-3\"
\n" ); document.write( "\"k=-9%2F4+%2B9%2F2+-3\"
\n" ); document.write( "\"k=9%2F4+%96+3\"
\n" ); document.write( "\"k=2.25-3\"
\n" ); document.write( "\"k=-0.75\"
\n" ); document.write( "vertex \"1.5\", \"-.75\" \r
\n" ); document.write( "\n" ); document.write( "table:
\n" ); document.write( "y = –x^2 + 3x – 3\r
\n" ); document.write( "\n" ); document.write( "x | y
\n" ); document.write( "0 | -3
\n" ); document.write( "1 | -1
\n" ); document.write( "2 | -1\r
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"-1x%5E2%2B3x%2B-3+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%283%29%5E2-4%2A-1%2A-3=-3\".
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\n" ); document.write( " The discriminant -3 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

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\n" ); document.write( " In the field of imaginary numbers, the square root of -3 is + or - \"sqrt%28+3%29+=+1.73205080756888\".
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\n" ); document.write( " The solution is
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\n" ); document.write( " Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B3%2Ax%2B-3+%29\"
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