document.write( "Question 39546: For quadratic functions, sketch two parabolas showing all procedures (concavity, y-intercepts, x-intercepts, symmetric axis and vertex point)\r
\n" ); document.write( "\n" ); document.write( "A) $\"y=+3x%5E2+-4x+%2B1\"$ \r
\n" ); document.write( "\n" ); document.write( "B) $\"y=+-2x%5E2+%2Bx+%2B1\"$ \n" ); document.write( "

Algebra.Com's Answer #25007 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
A)(y= 3x^2 -4x +1}}}
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"3x%5E2%2B-4x%2B1+=+0\"$ ) 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.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-4%29%5E2-4%2A3%2A1=4\"$ .
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\n" ); document.write( " Discriminant d=4 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--4%2B-sqrt%28+4+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+4+%29%29%2F2%5C3+=+1\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-4%29-sqrt%28+4+%29%29%2F2%5C3+=+0.333333333333333\"$
\n" ); document.write( "
\n" ); document.write( " Quadratic expression $\"3x%5E2%2B-4x%2B1\"$ can be factored:
\n" ); document.write( " $\"3x%5E2%2B-4x%2B1+=+3%28x-1%29%2A%28x-0.333333333333333%29\"$
\n" ); document.write( " Again, the answer is: 1, 0.333333333333333.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B1+%29\"$

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\n" ); document.write( "\n" ); document.write( "B) $\"y=+-2x%5E2+%2Bx+%2B1\"$
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"-2x%5E2%2B1x%2B1+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%281%29%5E2-4%2A-2%2A1=9\"$ .
\n" ); document.write( "
\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( " $\"x%5B1%5D+=+%28-%281%29%2Bsqrt%28+9+%29%29%2F2%5C-2+=+-0.5\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%281%29-sqrt%28+9+%29%29%2F2%5C-2+=+1\"$
\n" ); document.write( "
\n" ); document.write( " Quadratic expression $\"-2x%5E2%2B1x%2B1\"$ can be factored:
\n" ); document.write( " $\"-2x%5E2%2B1x%2B1+=+-2%28x--0.5%29%2A%28x-1%29\"$
\n" ); document.write( " Again, the answer is: -0.5, 1.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B1%2Ax%2B1+%29\"$

\n" ); document.write( "\n" ); document.write( "Hope this helps.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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