document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177821>Question 177821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Quadratic Equations<BR>\n" );
document.write( "Find the x-intercepts of each parabola.<BR>\n" );
document.write( "a) y=x^2-4x+4<BR>\n" );
document.write( "b) y=4x^2-12x+9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133486 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=133486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> </pre><font size=4><b><BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-4x%2B4 ALIGN=MIDDLE  ALT=\"y=x%5E2-4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factorable being a perfect square: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x-2%29=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x-2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "it shows you got X-intercept, (2,0)<BR>\n" );
document.write( "Let' see the vertex to see where we are, via Vertex Form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk2 ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We complete the square of the given eqn:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4x%2B4%29%2B4-4 ALIGN=MIDDLE  ALT=\"%28x%5E2-4x%2B4%29%2B4-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B0 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex exists @ (2,0)<BR>\n" );
document.write( "Letting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0%5E2-4%280%29%2B4 ALIGN=MIDDLE  ALT=\"y=0%5E2-4%280%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Y-Intercept<BR>\n" );
document.write( "Conclusion, given eqn it has ONLY X-Intercept because the vertex lies on the x-axis.<BR>\n" );
document.write( "As you see below;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-6%2C6%2C-6%2C6%2Cgrid%281%29%2Cgraph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2-4x%2B4%29%2Cgreen%28circle%280%2C4%2C.16%29%29%2Cblue%28circle%282%2C0%2C.16%29%29%2Cblue%28circle%282%2C0%2C.12%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x%5E2-12x%2B9 ALIGN=MIDDLE  ALT=\"y=4x%5E2-12x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For this solution toe xist, the discriminant should not be a negative number:<BR>\n" );
document.write( "By Quadratic so we can see the roots (X-intercepts):<BR>\n" );
document.write( "where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=4%2Cb=-12%2Cc=9%29 ALIGN=MIDDLE  ALT=\"system%28a=4%2Cb=-12%2Cc=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving for the discriminant: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%5E2-4ac=-12%5E2-4%2A4%2A0=144-144=0 ALIGN=MIDDLE  ALT=\"-b%5E2-4ac=-12%5E2-4%2A4%2A0=144-144=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The dicriminant is zero. Therefore, there's only one solution.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29=%28-%28-12%29%2B-sqrt%28-12%5E2-4%2A4%2A9%29%29%2F%282%2A4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2812%2B-sqrt%28144-144%29%29%2F8=%2812%2B-0%29%2F8=12%2F8=highlight%281.5=x%29 ALIGN=MIDDLE  ALT=\"x=%2812%2B-sqrt%28144-144%29%29%2F8=%2812%2B-0%29%2F8=12%2F8=highlight%281.5=x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%280%29%5E2-12%280%29%2B9 ALIGN=MIDDLE  ALT=\"y=4%280%29%5E2-12%280%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9 ALIGN=MIDDLE  ALT=\"y=9\"   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=drawing%28300%2C300%2C-3%2C5%2C-3%2C10%2Cgrid%281%29%2Cgraph%28300%2C300%2C-3%2C5%2C-3%2C10%2C4x%5E2-12x%2B9%29%2Cblue%28circle%281.5%2C0%2C.16%29%29%2Cblue%28circle%281.5%2C0%2C.12%29%29%2Cgreen%28circle%280%2C9%2C.16%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Jojo</pre><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );