document.write( "Question 177348: Could someone please help me answer this question?\r
\n" ); document.write( "\n" ); document.write( "If you are looking at a graph of a quadratic equation, how do\r
\n" ); document.write( "\n" ); document.write( "you determine where the solutions are? \n" ); document.write( "
Algebra.Com's Answer #132407 by gonzo(654)\"\" \"About 
You can put this solution on YOUR website!
the roots of the equation are the value of x when y = 0.
\n" ); document.write( "this equates to the point where the graph crosses the x-axis.
\n" ); document.write( "that's why when you want to solve for the roots of a quadratic equation, you set the equation equal to 0.
\n" ); document.write( "if the graph doesn't cross the x-axis, then it doesn't have real roots.
\n" ); document.write( "in that case, it will have imaginary roots.
\n" ); document.write( "the values you see on the graph conform to the values you calculate.
\n" ); document.write( "the general form of a quadratic equation is:
\n" ); document.write( "\"a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+y\"
\n" ); document.write( "to find the roots you set y equal to 0.
\n" ); document.write( "you get:
\n" ); document.write( "\"a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+0\"
\n" ); document.write( "to find the roots, you use the formula:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29\"
\n" ); document.write( "if \"sqrt%28b%5E2+-+4%2Aa%2Ac%29\" is positive, then you have real roots.
\n" ); document.write( "if it is negative, then you have imaginary roots.
\n" ); document.write( "you will only see the graph cross the x-axis if it has real roots.
\n" ); document.write( "here's a graph that has real roots.
\n" ); document.write( "\"x%5E2+%2B+2%2Ax+-+35\"
\n" ); document.write( "the graph looks like this:
\n" ); document.write( "\"graph%28800%2C300%2C-10%2C%2B10%2C-40%2C20%2Cx%5E2%2B2%2Ax-35%29\"
\n" ); document.write( "the roots are x = 5, and x = -7
\n" ); document.write( "here's a graph that has imaginary roots.
\n" ); document.write( "\"x%5E2+%2B+2%2Ax+%2B+2\"
\n" ); document.write( "the graph looks like this:
\n" ); document.write( "\"graph%28800%2C300%2C-10%2C%2B10%2C-20%2C20%2Cx%5E2%2B2%2Ax%2B2%29\"
\n" ); document.write( "the graph with imaginary roots did not cross the x-axis. \n" ); document.write( "
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