document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=273706>Question 273706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "I'm having trouble with the following question...\r<BR>\n" );
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document.write( "Find the x- and y- coordinates of the parabola vertex for the function<BR>\n" );
document.write( "f(x)=-3x^2+6x-1\r<BR>\n" );
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document.write( "My textbook tells me to + and - the coefficient of x\r<BR>\n" );
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document.write( "So I do this...<BR>\n" );
document.write( "f(x)=-3x^2+6x-1<BR>\n" );
document.write( "f(x)=-3x^2+6x+3-3-1<BR>\n" );
document.write( "f(x)=(-3x^2+6x+3)-3-1\r<BR>\n" );
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document.write( "And now I need to factor and simplify\r<BR>\n" );
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document.write( "any help appreciated.\r<BR>\n" );
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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 #199918 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=199918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation is:\r<BR>\n" );
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document.write( "f(x)=-3x^2+6x-1 \r<BR>\n" );
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document.write( "The vertex is at x = -b/2a\r<BR>\n" );
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document.write( "since this equations is in the standard form of ax^2 + bx + c, then:\r<BR>\n" );
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document.write( "a = -3<BR>\n" );
document.write( "b = 6<BR>\n" );
document.write( "c = -1\r<BR>\n" );
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document.write( "vertex is at x = -b/2a = -6/-6 = 1.\r<BR>\n" );
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document.write( "the y coordinate is at y = f(1) = -3*1^2 + 6*1 - 1 = -3 + 6 -1 = 2\r<BR>\n" );
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document.write( "the vertex should be at (x,y) = (1,2)\r<BR>\n" );
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document.write( "graph of this equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28600%2C600%2C-10%2C10%2C-10%2C10%2C-3x%5E2%2B6x-1%29 ALIGN=MIDDLE  ALT=\"graph+%28600%2C600%2C-10%2C10%2C-10%2C10%2C-3x%5E2%2B6x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "looking at the graph, this appears to be accurate.\r<BR>\n" );
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document.write( "the vertex is the max/min point and it is at (x,y) = (1,2) as predicted by the formula.\r<BR>\n" );
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document.write( "I'm not exactly sure of what your textbook is telling you and why.\r<BR>\n" );
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document.write( "The vertex is found by the formula I just showed you if this is a quadratic equation.\r<BR>\n" );
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document.write( "If you are looking for the roots of the equation, those roots can be found by factoring the equation or by the use of the quadratic formula.\r<BR>\n" );
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document.write( "the equation is, once again, -3x^2 + 6x - 1\r<BR>\n" );
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document.write( "I don't believe the roots can be found by factoring, so you would have to resort to the quadratic formula or the completing the squares method.\r<BR>\n" );
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document.write( "The roots of the equation are the points at which the graph crosses the x-axis.\r<BR>\n" );
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document.write( "You can see from the graph that those roots should be around .1 and 1.8.\r<BR>\n" );
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document.write( "I could solve for them, but I believe the questions was to find the vertex, which I did for you above.\r<BR>\n" );
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document.write( "The quadratic formula to find the roots is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as before, the equation is in standard form of f(x) = -3x^2 - 6x + 1 and:\r<BR>\n" );
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document.write( "a = -3<BR>\n" );
document.write( "b = -6<BR>\n" );
document.write( "c = 1\r<BR>\n" );
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document.write( "You just plug those values into the quadratic formula and  you find the x value of your roots, if the values are real.\r<BR>\n" );
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document.write( "If the values are imaginary or complex, then the roots are not real and the graph of the equation will not cross the x-axis.\r<BR>\n" );
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document.write( "This equation has real roots as can be seen from the graph.\r<BR>\n" );
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document.write( "I have no idea what your textbook is telling you.\r<BR>\n" );
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document.write( "If the equation is symmetric than f(x) = f(-x) which means that you have an axis of symmetry and your graph will have values to the left of that axis and to the right of that axis.\r<BR>\n" );
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document.write( "But that's another topic.\r<BR>\n" );
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document.write( "The answer to your question (I think) is that the vertex of the equation is at the point (x,y) = (1,2) as can be confirmed by looking at the graph.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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