document.write( "Question 248955: Find the x- and y-intercepts. If no x-intercepts exist, state so.\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29+=+2x2+-+2x+-+24\"
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Algebra.Com's Answer #181390 by oberobic(2304)\"\" \"About 
You can put this solution on YOUR website!
\"f%28x%29+=+2x2+-+2x+-+24\"
\n" ); document.write( "\"f%28x%29+=+2%28x2+-+x+-+12%29\"
\n" ); document.write( "\"f%28x%29+=+2%28x-4%29%28x%2B3%29\"
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\n" ); document.write( "y-intercept is defined by f(0).
\n" ); document.write( "It is where the line crosses the y-axis.
\n" ); document.write( "\"f%280%29+=+2%280-4%29%280%2B3%29\"
\n" ); document.write( "\"f%280%29+=+-8%2A3+=+-24\"
\n" ); document.write( ".
\n" ); document.write( "x-intercept is defined by f(x) = 0.
\n" ); document.write( "It is where the line crosses the x-axis.
\n" ); document.write( "Recall
\n" ); document.write( "\"f%28x%29+=+2%28x-4%29%28x%2B3%29\"
\n" ); document.write( "If x=4, then the entire right-hand side = 0, so that is an x-intercept.
\n" ); document.write( "If x=-3, then the entire right-hand side = 0, so that is another x-intercept.
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\n" ); document.write( "The graph is useful to review. It is a parabola.
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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%2B-2x%2B-24+=+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%2A2%2A-24=196\".
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\n" ); document.write( " Discriminant d=196 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--2%2B-sqrt%28+196+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+196+%29%29%2F2%5C2+=+4\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-2%29-sqrt%28+196+%29%29%2F2%5C2+=+-3\"
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\n" ); document.write( " Quadratic expression \"2x%5E2%2B-2x%2B-24\" can be factored:
\n" ); document.write( " \"2x%5E2%2B-2x%2B-24+=+2%28x-4%29%2A%28x--3%29\"
\n" ); document.write( " Again, the answer is: 4, -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+2%2Ax%5E2%2B-2%2Ax%2B-24+%29\"
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