document.write( "Question 40444: Find the axis of symmetry
\n" ); document.write( "y=-x^2-x-7 \n" ); document.write( "

Algebra.Com's Answer #25804 by Nate(3500) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"y=-x%5E2-x-7\"$
\n" ); document.write( "Axis of symmetry: $\"x+=+-b%2F%282a%29\"$
\n" ); document.write( " $\"x+=+1%2F%282%28-1%29%29\"$
\n" ); document.write( " $\"x+=+-1%2F2\"$
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"-1x%5E2%2B-1x%2B-7+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-1%29%5E2-4%2A-1%2A-7=-27\"$ .
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\n" ); document.write( " The discriminant -27 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 -27 is + or - $\"sqrt%28+27%29+=+5.19615242270663\"$ .
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\n" ); document.write( " The solution is

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\n" ); document.write( " Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-1%2Ax%2B-7+%29\"$

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