document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=284186>Question 284186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Discuss two examples where you use a quadratic function and another where you use a radical equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206389 by </B><A HREF=/tutors/aboutme.mpl?userid=alex224><B>alex224(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alex224><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=206389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard form of a quadratic function is y = ax^2 + bx + c or f(x) = ax^2 + bx + c where x is the independent variable, y is the dependent variable, and a, b, and c are all constants.\r<BR>\n" );
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document.write( "An example of how to solve one of these problems is:\r<BR>\n" );
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document.write( "y=x^2-5x-14\r<BR>\n" );
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document.write( "1.)Set y equal to zero to find the x-intercepts<BR>\n" );
document.write( "0=x^2-5x-14\r<BR>\n" );
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document.write( "2.)Next you need to factor <BR>\n" );
document.write( "0=(x-7)(x+2)\r<BR>\n" );
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document.write( "3.)Then set each factor eqaul to zero <BR>\n" );
document.write( "0=x-7 0=x+2\r<BR>\n" );
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document.write( "4.)Solve<BR>\n" );
document.write( "x=7,-2\r<BR>\n" );
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document.write( "Sometimes the function is not factorable and in that case you need to use the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here is an example of a problem that needs to be solved by using the quadratic formula:\r<BR>\n" );
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document.write( "y=2x^2+4x-5\r<BR>\n" );
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document.write( "1.)First you need to set the function equal to zero:<BR>\n" );
document.write( "0=2x^2+4x-5\r<BR>\n" );
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document.write( "2.)Then you need to determine the variables and plug them into the qudratic equation:<BR>\n" );
document.write( "a=2<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "c=-5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A2%2A-5+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A2%2A-5+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+16%2B40+%29%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+16%2B40+%29%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+56%29%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+56%29%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4.) Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+sqrt%28+14%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+14%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "5.)Final Answer\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1+-+sqrt%28+14%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"%28-1+-+sqrt%28+14%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0),(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-1+%2B+sqrt%28+14%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+%28-1+%2B+sqrt%28+14%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,0)\r<BR>\n" );
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document.write( "A radical equation is an equation that involves at least one expression or variable under a  radical.  \r<BR>\n" );
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document.write( "To solve these types of equations you need to isolate the variable by doing the opposite operation.  \r<BR>\n" );
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document.write( "Here is an example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+sqrt%28+x%29%29+ ALIGN=MIDDLE  ALT=\"%28+sqrt%28+x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=4\r<BR>\n" );
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document.write( "In order to get the answer you need to do the opposite of taking the root which is squaring, so you need to sqaure both sides of the equation.\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+sqrt%28+x%29%29+ ALIGN=MIDDLE  ALT=\"%28+sqrt%28+x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >)^2=(4)^2\r<BR>\n" );
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document.write( "The final answer is x=16\r<BR>\n" );
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