document.write( "Question 145458: Please find the -y intercept
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\n" ); document.write( " and line of symetry of the following quadratics.
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\n" ); document.write( "\n" ); document.write( " 1.\"y=x%5E2%2B2x%2B12\"
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\n" ); document.write( "\n" ); document.write( " 2.\"y=x%5E2-6x%2B5\"\r
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\n" ); document.write( "\n" ); document.write( " 3.\"y=x%5E2-8x%2B15\"
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Algebra.Com's Answer #106190 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
The y intercept is at x = 0. f(0) is:
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\n" ); document.write( "2. 5
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\n" ); document.write( "\n" ); document.write( "1. \"y+=+x%5E2%2B2x%2B12+=+0\"
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B2x%2B12+=+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=%282%29%5E2-4%2A1%2A12=-44\".
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\n" ); document.write( " The discriminant -44 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 -44 is + or - \"sqrt%28+44%29+=+6.6332495807108\".
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\n" ); document.write( " The solution is , or
\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%2B2%2Ax%2B12+%29\"

\n" ); document.write( "\n" ); document.write( "2. \"x%5E2-6x%2B5=0\"
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-6x%2B5+=+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=%28-6%29%5E2-4%2A1%2A5=16\".
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\n" ); document.write( " Discriminant d=16 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--6%2B-sqrt%28+16+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+5\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-6%29-sqrt%28+16+%29%29%2F2%5C1+=+1\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-6x%2B5\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-6x%2B5+=+%28x-5%29%2A%28x-1%29\"
\n" ); document.write( " Again, the answer is: 5, 1.\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%2B-6%2Ax%2B5+%29\"

\n" ); document.write( "\n" ); document.write( "3. \"x%5E2-8x%2B15=0\"
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-8x%2B15+=+0\") has the following solutons:
\n" ); document.write( "
\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-8%29%5E2-4%2A1%2A15=4\".
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\n" ); document.write( " Discriminant d=4 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--8%2B-sqrt%28+4+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+5\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-8%29-sqrt%28+4+%29%29%2F2%5C1+=+3\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-8x%2B15\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-8x%2B15+=+%28x-5%29%2A%28x-3%29\"
\n" ); document.write( " Again, the answer is: 5, 3.\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%2B-8%2Ax%2B15+%29\"

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