document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141449>Question 141449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y=2x^2+4X-6, find x&y intercepts, coordinates of vertex,graph equation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103072 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=103072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the intercepts, we will first set x=0 and then y=0:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6 ALIGN=MIDDLE  ALT=\"y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- y-intercept<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2x%5E2%2B4x-6 ALIGN=MIDDLE  ALT=\"0=2x%5E2%2B4x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we need to solve the second equation:<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%282x-2%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"0=%282x-2%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This can only be when x=1 or x=-3. <---x-intercepts\r<BR>\n" );
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document.write( "The vertex is where the function is at a minimum. I will give you a little calculus after this, but it suffices to say that the vertex is x=-b/(2a)  when given a polynomial of form ax^2+bx+c. So the vertex per that formula is: x=-4/4=-1<BR>\n" );
document.write( "which gives a y value of 2-4-6=-8. The ordered pair, then, is (-1,-8).\r<BR>\n" );
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document.write( "Calculus:<BR>\n" );
document.write( "We find the critical points: <BR>\n" );
document.write( "f'(x)=4x+4<BR>\n" );
document.write( "0=4x+4<BR>\n" );
document.write( "-->x=-1<BR>\n" );
document.write( "We then proceed as before, finding that the ordered pair is (-1,-8).\r<BR>\n" );
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document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-5%2C+5%2C+-10%2C+10%2C+2x%5E2%2B4x-6+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-5%2C+5%2C+-10%2C+10%2C+2x%5E2%2B4x-6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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