document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176168>Question 176168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> this is one question with different parts <BR>\n" );
document.write( "Find the vertex, line of symmetry, maximum or minimum value of the quadratic function, and graph the function.<BR>\n" );
document.write( "f(x)=-2x^2+2x+3<BR>\n" );
document.write( "x-coordinate of vertex<BR>\n" );
document.write( "y-coordinate of vertex<BR>\n" );
document.write( "equation of line of symmetry<BR>\n" );
document.write( "max/min value of f(x)<BR>\n" );
document.write( "The value of f(1/2)=7/2 is min or max<BR>\n" );
document.write( "Please help I have no idea what I am doing 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 #131247 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=131247\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you have a function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you have a parabola with vertex at the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-b/2a,f(-b/2a)\right)\"> \r<BR>\n" );
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document.write( "So, calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F2a ALIGN=MIDDLE  ALT=\"-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the x-coordinate of the vertex.  Then substitute that x-coordinate value into the function and calculate the y-coordinate of the vertex.\r<BR>\n" );
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document.write( "The axis of symmetry is the vertical line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+v ALIGN=MIDDLE  ALT=\"x+=+v\"   DISABLED_style= \"max-width:90%; height:auto;\" > where v is equal to the x-coordinate of the vertex, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+-b%2F2a ALIGN=MIDDLE  ALT=\"v+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If the lead coefficient, in other words the coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is positive, then the parabola is concave up and the vertex is a minimum.  If the lead coefficient is negative, then the parabola is concave down and the vertex is a maximum.\r<BR>\n" );
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document.write( "To graph the function, first plot the vertex point.  Then add a convenient value to the x-coordinate and recalculate the value of the function to get another point on the graph.  Because of symmetry, you will also have the same value of the function when you subtract the same amount from the x-coordinate.  Perform this process 3 or 4 times to get a set of points and then draw a smooth curve through the plotted points.\r<BR>\n" );
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document.write( "Your graph should look like this:\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-2x%5E2%2B2x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-2x%5E2%2B2x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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