document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=331602>Question 331602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for the provided quadratic function of <BR>\n" );
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document.write( "A. Find the vertex\r<BR>\n" );
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document.write( "B. find the y intercept\r<BR>\n" );
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document.write( "C. find the x-intercepts\r<BR>\n" );
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document.write( "D. graph function </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #237683 by </B><A HREF=/tutors/aboutme.mpl?userid=texttutoring><B>texttutoring(324)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=texttutoring><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/cgi-bin/show-face.mpl?user=texttutoring><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=237683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This equation is a parabola in general form. The easiest way to graph it is to convert it to standard form, y=a(x-p)^2 + q. You can do this by completing the square:\r<BR>\n" );
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document.write( "Halve the b term (b=4 in your equation) and then square it: (4/2)^2 = 2^2 = 4\r<BR>\n" );
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document.write( "Add this number to the first 2 terms, but then subtract it at the end (so that you are just adding zero to the overall equation):\r<BR>\n" );
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document.write( "y=x^2 +4x + 4  + 3  - 4<BR>\n" );
document.write( "y=(x^2+4x+4) +3-4<BR>\n" );
document.write( "y=(x+2)^2 -1\r<BR>\n" );
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document.write( "Now the equation is in standard form, y=a(x-p)^2 + q. The vertex is at (p,q)=(-2,-1).\r<BR>\n" );
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document.write( "You can find the y=intercept by setting x=0 and solving for y. It's easiest to do this with the general form:\r<BR>\n" );
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document.write( "y=x^2+4x+3<BR>\n" );
document.write( "y = 0+)+3<BR>\n" );
document.write( "y=3\r<BR>\n" );
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document.write( "The y-intercept is y=3.\r<BR>\n" );
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document.write( "To find the x-intercepts, factor, set y=0 and solve for x. You have to solve by factoring:\r<BR>\n" );
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document.write( "y=x^2+4x+3<BR>\n" );
document.write( "0 = x^2+4x+3<BR>\n" );
document.write( "0 = (x+3)(x+1)\r<BR>\n" );
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document.write( "Which means that the x-intercepts are x= -3, and x= -1.\r<BR>\n" );
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document.write( "You now know the x-intercepts, y-intercept, and vertex. You should be able to just connect the dots to graph the equation.\r<BR>\n" );
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document.write( "It should look like this: http://www.wolframalpha.com/input/?i=y%3Dx^2%2B4x%2B3 </SPAN>\n" );
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