document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=223764>Question 223764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a parabola has a vertx (-1,8) and y-intercept 7<BR>\n" );
document.write( "How do you find the function f whose graph is this parabola and express f in the form f(x)= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167263 by </B><A HREF=/tutors/aboutme.mpl?userid=MLipsky><B>MLipsky(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MLipsky><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=167263\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can write a quadratic equation in \"vertex form\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-k=a%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"y-k=a%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where the vertex is (h, k).\r<BR>\n" );
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document.write( "The answer will still have \"x\" and \"y\" in the equation, so we just need to find the \"a\", \"h\" and \"k\".<BR>\n" );
document.write( "You already have the \"h\" and \"k\" (from the vertex).  So, let's plug them in:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%288%29=a%28x-%28-1%29%29%5E2 ALIGN=MIDDLE  ALT=\"y-%288%29=a%28x-%28-1%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=a%28x%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"y-8=a%28x%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (simplified)\r<BR>\n" );
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document.write( "Looking good, but we still need \"a\".  Now, where in the world are we going to find THAT???\r<BR>\n" );
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document.write( "Wait.  I have an idea.  They said the y-intercept is 7.  In other words, it crosses the y-axis at y=7.  Hey!  They just gave us another ordered pair:  (0, 7).\r<BR>\n" );
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document.write( "Let's plug that in:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-8=a%280%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"7-8=a%280%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (plugged in)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=a%281%29%5E2 ALIGN=MIDDLE  ALT=\"-1=a%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=a%281%29 ALIGN=MIDDLE  ALT=\"-1=a%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=a ALIGN=MIDDLE  ALT=\"-1=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have all three pieces of our puzzle:<BR>\n" );
document.write( "a=-1<BR>\n" );
document.write( "h=-1<BR>\n" );
document.write( "k=8\r<BR>\n" );
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document.write( "Plug in the pieces:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=-1%28x%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"y-8=-1%28x%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Notice that the answer still has \"x\" and \"y\" in the equation.)\r<BR>\n" );
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document.write( "Oops!  They want the answer in standard form.  No problem.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=-1%28x%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"y-8=-1%28x%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=-1%28x%2B1%29%2A%28x%2B1%29 ALIGN=MIDDLE  ALT=\"y-8=-1%28x%2B1%29%2A%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (squared the (x+1) )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=-1%28x%5E2%2B2%2Ax%2B1%29 ALIGN=MIDDLE  ALT=\"y-8=-1%28x%5E2%2B2%2Ax%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (F.O.I.L.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-8=-x%5E2-2%2Ax-1%29 ALIGN=MIDDLE  ALT=\"y-8=-x%5E2-2%2Ax-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (distributed the -1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%5E2-2%2Ax%2B7%29 ALIGN=MIDDLE  ALT=\"y=-x%5E2-2%2Ax%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (added 8 to both sides)\r<BR>\n" );
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document.write( "Let's graph it just to be sure the vertex is at (-1, 8) and y-intercept is at 7.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E2%2B-2%2Ax%2B7%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E2%2B-2%2Ax%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Shazam!  It checks out.\r<BR>\n" );
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document.write( "<hr />For more worked problems, or tutoring, please visit <a  rel=nofollow HREF=\"http://www.mathlocker.com\">MathLocker.com</a>.<hr /> </SPAN>\n" );
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