document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155562>Question 1155562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of a quadratic function in vertex form with a vertex at(0,5) and contains the point(1,-2)?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778154 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=778154\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "With the vertex on the y-axis at (0,5), the equation is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2%2B5 ALIGN=MIDDLE  ALT=\"y+=+ax%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To find the coefficient a and thus find the equation, plug in the coordinates of the other given point.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+a%281%5E2%29%2B5 ALIGN=MIDDLE  ALT=\"-2+=+a%281%5E2%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+a%2B5 ALIGN=MIDDLE  ALT=\"-2+=+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+=+-7 ALIGN=MIDDLE  ALT=\"a+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-7x%5E2%2B5 ALIGN=MIDDLE  ALT=\"y+=+-7x%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "There is another less formal method for finding the coefficient a which you can use if you understand parabolas and quadratic functions.  The equation<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2%2B5 ALIGN=MIDDLE  ALT=\"y+=+ax%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "tells you that the displacement in y is a times the displacement in x.  From (0,5) to (1,-2) the displacement in x is 1; the square of that is 1.  And the corresponding displacement in y is -7; -7 is -7 times 1, so a is -7.<br><BR>\n" );
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