document.write( "Question 268037: If you are looking at a graph of a quadratic equation, how do you determine where the solutions are? If you have any examples to provide, that would also be helpful. Thanks! \n" ); document.write( "
Algebra.Com's Answer #196525 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
The solutions are where y=0 \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%2B-2x%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=%28-2%29%5E2-4%2A1%2A-3=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--2%2B-sqrt%28+16+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+3\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-2%29-sqrt%28+16+%29%29%2F2%5C1+=+-1\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-2x%2B-3\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-2x%2B-3+=+1%28x-3%29%2A%28x--1%29\"
\n" ); document.write( " Again, the answer is: 3, -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-2%2Ax%2B-3+%29\"

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