document.write( "Question 172244This question is from textbook Introductory Algebra
\n" ); document.write( ": Graph the quadratic equation. Label the ordered pairs for the vertex and the y-intercept.\r
\n" ); document.write( "\n" ); document.write( "y = x^2 + x -2 \n" ); document.write( "

Algebra.Com's Answer #127237 by KnightOwlTutor(293) $\"\"$ $\"About$

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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B1x%2B-2+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%281%29%5E2-4%2A1%2A-2=9\"$ .
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\n" ); document.write( " Discriminant d=9 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28-1%2B-sqrt%28+9+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%281%29%2Bsqrt%28+9+%29%29%2F2%5C1+=+1\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%281%29-sqrt%28+9+%29%29%2F2%5C1+=+-2\"$
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\n" ); document.write( " Quadratic expression $\"1x%5E2%2B1x%2B-2\"$ can be factored:
\n" ); document.write( " $\"1x%5E2%2B1x%2B-2+=+1%28x-1%29%2A%28x--2%29\"$
\n" ); document.write( " Again, the answer is: 1, -2.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-2+%29\"$

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\n" ); document.write( "\n" ); document.write( "The lowest point is the vertex. \n" ); document.write( "

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