document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622852>Question 622852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation of the quadratic function with roots 0 and 2 and a vertex at (1,5)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391696 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=391696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there - <BR>\n" );
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document.write( "One way to solve this problem is to write the equation in vertex form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When a quadratic is in this form, the point (h,k) is the vertex of the parabola. We know that the vertex of the parabola is (h,k)=(1,5).<BR>\n" );
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document.write( "Substitute those known values for h and k in the equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-1%29%5E2%2B5 ALIGN=MIDDLE  ALT=\"y=a%28x-1%29%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We know that two roots of the quadratic are 0 and 2. Roots of a quadratic are points where the graph crosses the x-axis. Thus the points (0,0) and (2,0) are on the parabola.<BR>\n" );
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document.write( "We can substitute one of these points for x and y in our equation. Then we can solve for a. Arbitrarily, I'll choose the point (0,0). Either point will work.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-1%29%5E2%2B5 ALIGN=MIDDLE  ALT=\"y=a%28x-1%29%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%280-1%29%5E2%2B5 ALIGN=MIDDLE  ALT=\"0=a%280-1%29%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify and solve for a.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%28-1%29%5E2%2B5 ALIGN=MIDDLE  ALT=\"0=a%28-1%29%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%2B5 ALIGN=MIDDLE  ALT=\"0=a%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-5 ALIGN=MIDDLE  ALT=\"a=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The equation for this quadratic is<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%28x-1%29%5E2%2B5 ALIGN=MIDDLE  ALT=\"y=-5%28x-1%29%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Feel free to email me if you have questions about this solution.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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