document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192072>Question 1192072</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the quadratic function satisfying the given conditions. ​(​Hint: Determine values of​ a, h, and k that satisfy ​P(x)​=a(x-​h)^2+​k.) Express the answer in the form ​P(x)=ax^2+bx+c. Use a calculator to support the result.<BR>\n" );
document.write( "Vertex (-1,-5); through (6,93)<BR>\n" );
document.write( "p(x)=<BR>\n" );
document.write( "(simplify your answer) <BR>\n" );
document.write( "thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823969 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=823969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Vertex = (h,k) = (-1,-5)\r<BR>\n" );
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document.write( "y = a(x-h)^2 + k .... vertex form<BR>\n" );
document.write( "y = a(x-(-1))^2 + (-5)<BR>\n" );
document.write( "y = a(x+1)^2 - 5<BR>\n" );
document.write( "That's the result so far after plugging in the h,k values mentioned.\r<BR>\n" );
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document.write( "Now let's plug in the coordinates of the other point that's on the parabola.<BR>\n" );
document.write( "The goal is to isolate 'a'<BR>\n" );
document.write( "y = a(x+1)^2 - 5<BR>\n" );
document.write( "93 = a(6+1)^2 - 5<BR>\n" );
document.write( "93 = a(7)^2 - 5<BR>\n" );
document.write( "93 = a(49) - 5<BR>\n" );
document.write( "93 = 49a - 5<BR>\n" );
document.write( "49a - 5 = 93<BR>\n" );
document.write( "49a = 93+5<BR>\n" );
document.write( "49a = 98<BR>\n" );
document.write( "a = 98/49<BR>\n" );
document.write( "a = 2\r<BR>\n" );
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document.write( "The fully updated vertex form equation is<BR>\n" );
document.write( "y = 2(x+1)^2 - 5\r<BR>\n" );
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document.write( "Expand things out and simplify.<BR>\n" );
document.write( "y = 2(x+1)^2 - 5<BR>\n" );
document.write( "y = 2(x^2+2x+1) - 5<BR>\n" );
document.write( "y = 2x^2+4x+2 - 5<BR>\n" );
document.write( "y = 2x^2+4x-3\r<BR>\n" );
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document.write( "We arrive at the form ax^2+bx+c, such that,<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "b = 4<BR>\n" );
document.write( "c = -3\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "P(x) = 2x^2+4x-3<BR>\n" );
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