document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=705760>Question 705760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Someone PLEASE help me!I'm am all sorts of confused on these. Can anyone help me out and show me how do get to these? \r<BR>\n" );
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document.write( "1. Given the following quadratic equation, find<BR>\n" );
document.write( "a. the vertex<BR>\n" );
document.write( "b. the axis of symmetry<BR>\n" );
document.write( "c. the intercepts<BR>\n" );
document.write( "d. the domain<BR>\n" );
document.write( "e. the range<BR>\n" );
document.write( "f. the interval where the function is increasing, and<BR>\n" );
document.write( "g. the interval where the function is decreasing<BR>\n" );
document.write( "h. Graph the function.\r<BR>\n" );
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document.write( "y=-x^2+2x+8\r<BR>\n" );
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document.write( "2.  Given the following rational function, find <BR>\n" );
document.write( "a. the horizontal asymptote(s),  <BR>\n" );
document.write( "b. the vertical asymptote(s), if any, and<BR>\n" );
document.write( "c. the oblique asymptote(s), if any.<BR>\n" );
document.write( "f(x)=6/(x-5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434869 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=434869\">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( "Given the quadratic function <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\ =\ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "First, determine the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">-coordinate of the vertex.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_v\ =\ \frac{-b}{2a}\">\r<BR>\n" );
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document.write( "Then determine the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-coordinate of the vertex.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y_v\ =\ y(x_v)\ =\ a(x_v)^2\ +\ b(x_v)\ +\ c\">\r<BR>\n" );
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document.write( "Then determine the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-coordinate of the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-intercept which is equal to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y(0)\ =\ a(0)^2\ +\ b(0)\ +\ c\ =\ c\">\r<BR>\n" );
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document.write( "Then set the function equal to zero and solve the resulting quadratic equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ ax^2\ +\ bx\ +\ c\ =\ 0\ \Right\ x_1\ =\ \frac{-b\ +\ \sqrt{b^2\ -\ 4ac}}{2a},\ x_2\ =\ \frac{-b\ -\ \sqrt{b^2\ -\ 4ac}}{2a}\">\r<BR>\n" );
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document.write( "Then determine whether the graph opens upwards or downwards.  If the lead coefficient, that is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a\"> is positive, the graph opens upward, otherwise it opens downward.\r<BR>\n" );
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document.write( "With the above information you can answer all of the questions:\r<BR>\n" );
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document.write( "1.  Vertex:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_v,\,y_v\right)\">\r<BR>\n" );
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document.write( "2.  Axis of symmetry:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ =\ x_v\">\r<BR>\n" );
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document.write( "3.  Intercepts:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(0,\,c\right)\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \left(x_1,\,0\right)\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_2,\,0\right)\">\r<BR>\n" );
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document.write( "4.  Domain:  The domain of all polynomial functions is the set of real numbers.\r<BR>\n" );
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document.write( "5.  Range:  If the graph opens upward, then the range is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \{y\,\in\,\mathbb{R}|\,y\ \geq y_v\}\">.  If the graph opens downward, then the range is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \{y\,\in\,\mathbb{R}|\,y\ \leq y_v\}\">\r<BR>\n" );
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document.write( "6.  Increasing interval:  if graph opens upward, the increasing interval is from <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y_v\"> to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \infty\">.  If the graph opens downward, the increasing interval is from <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\infty\"> to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y_v\">.\r<BR>\n" );
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document.write( "7.  Decreasing interval:  reverse the answers to 6. above.\r<BR>\n" );
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document.write( "8.  Plot the vertex, the y-intercept, and the two x-intercepts.  Use symmetry to plot <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(2x_v,c\right)\">.  Draw a smooth curve through the 5 plotted points.\r<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( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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