document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167615>Question 1167615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> https://answers.yahoo.com/question/index?qid=20201018140421AAedVNb </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792232 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your problem is shown below:\r<BR>\n" );
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document.write( "let y = f(x).<BR>\n" );
document.write( "the function becomes y = -x^2 + 8x - 7\r<BR>\n" );
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document.write( "the standard form of a quadratic equation is y = ax^2 + bx + c<BR>\n" );
document.write( "a is the coefficient of the x^2 term.<BR>\n" );
document.write( "b is the coefficient of the x term.<BR>\n" );
document.write( "c is the constant term.\r<BR>\n" );
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document.write( "the standard form of the equation becomes y = -x^2 + 8x - 7\r<BR>\n" );
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document.write( "the vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.<BR>\n" );
document.write( "a is the coefficient of the x^2 term,<BR>\n" );
document.write( "(h,k) is the coordinates of the vertex.\r<BR>\n" );
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document.write( "from the standard form of the equation, you would solve for the x-coordinate of the vertex by the following equation:<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "when b = 8 and a = -1, this becomes x = -8/(-2) = 4.<BR>\n" );
document.write( "the y-coordinate of the vertex is found by replacing x in the standard form of the equation by 4 and solving for y.<BR>\n" );
document.write( "you get y = -4^2 + 8*4 - 7 which becomes y = -16 + 32 - 7.<BR>\n" );
document.write( "solve for y to get y = 9.\r<BR>\n" );
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document.write( "the vertex from the standard form of the equation is (x,y) = (4,9).<BR>\n" );
document.write( "the vertex from the vertex form of the equation is (h,k) = (4,9).\r<BR>\n" );
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document.write( "the vertex form of the equation becomes y = -1 * (x-4)^2 + 9.\r<BR>\n" );
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document.write( "both standard form of the equation and vertex form of the equation can be seen in the following graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/101807.jpg\" >\r<BR>\n" );
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document.write( "since both equations are equivalent, they both draw the same graph.\r<BR>\n" );
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document.write( "when you bring the equations down 5 units, you just subtract 5 from the constant term in the standard equation and you drop 5 from the value of k in the vertex form of the equation.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "y = -x^2 + 8x - 12 in the standard form.<BR>\n" );
document.write( "y = -(x-4)^2 + 4 in the vertex form.\r<BR>\n" );
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document.write( "both standard form of the equation and vertex form of the equation can be seen in the following graph.\r<BR>\n" );
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document.write( "you can see from both graphs that the vertex was dropped 5 units from (4,9) to (4,4).\r<BR>\n" );
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document.write( "here's a reference you might find helpful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php\" target = \"_blank\">https://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php</a>\r<BR>\n" );
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