document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120339>Question 1120339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4.  Determine the quadratic function f whose graph is given.&#8195;&#8195;<BR>\n" );
document.write( "The vertex is (3,-4) and the other given point is (1,4)\r<BR>\n" );
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document.write( "6.  g(x) = 1/5 x -4, Determine the slope and y-intercept of the function., Use the slope and y-intercept to graph the linear function. Determine the average rate of change of the function. Determine whether the linear function is increasing, decreasing, or constant\r<BR>\n" );
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document.write( "9.  Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function.<BR>\n" );
document.write( "G(x) = x^4 – 1 / 3x^2 – 3x\r<BR>\n" );
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document.write( "7.  Analyze the polynomial function f(x)= (x+3)^2 (x-6)^2<BR>\n" );
document.write( "Determine the end behavior of the graph of the function.<BR>\n" );
document.write( "Find the x- and y-intercepts of the graph of the function.<BR>\n" );
document.write( "Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept.<BR>\n" );
document.write( "Determine the maximum number of turning points on the graph of the function.<BR>\n" );
document.write( "Use the above information to draw a complete graph of the function.\r<BR>\n" );
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document.write( "sorry its so many, I worked the problems some came up wrong, I need to see the steps to pls and 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 #736006 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Post each question separately.  Show the work you have done.  Describe what it is that is causing you difficulty.\r<BR>\n" );
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document.write( "I'll help with the first one here.\r<BR>\n" );
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document.write( "4.  You are given two points on a graph and asked for the quadratic function.  In order to uniquely determine a quadratic, you need three points.  That is because, in general, to uniquely determine a polynomial function of degree <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> you need <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ +\ 1\"> points.\r<BR>\n" );
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document.write( "Fortunately, one of the given points is identified as the vertex of the parabola graph.  So, by symmetry, a third point can be determined.  The vertex is at (3,-4) and the other point, (1, 4) is 2 units distant in the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-axis.  Hence there is another point on the parabola 2 units on the other side of the vertex with a function value of 4, namely the point (5, 4).\r<BR>\n" );
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document.write( "We begin with the general quadratic function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "Since the point (1, 4) is on the graph, the following must be true about the desired function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(1)\ =\ 4\">\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a(1)^2\ +\ b(1)\ +\ c\ =\ 4\">\r<BR>\n" );
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document.write( "which simplifies to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ =\ 4\">\r<BR>\n" );
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document.write( "Similarly, since we know that (3,-4) and (5,4) are on the graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9a\ +\ 3b\ +\ c\ =\ -4\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25a\ +\ 5b\ +\ c\ =\ 4\">\r<BR>\n" );
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document.write( "We now have a 3X3 linear system.  All you need to do is solve the 3X3 system to obtain the necessary coefficients for your function.  Hint:  Use the MDETERM function in Excel (or Numbers if you are on a Mac) to find the values of the four determinants necessary to solve the system using Cramer's Rule.  There are also several online linear system solvers available.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=QuadFunctionFrom2Points.jpg\">.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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