document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71903>Question 71903</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321292642/algebrahomeworkh>algebra and trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=5x^2-10x+3\r<BR>\n" );
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document.write( "a. find the vertex<BR>\n" );
document.write( "b. find the axis of symmetry<BR>\n" );
document.write( "c. determine whether there is a maximum or minimum value and find the value<BR>\n" );
document.write( "d. find the range<BR>\n" );
document.write( "e graph the function\r<BR>\n" );
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document.write( "I would really appreciate some help with this question. I don't understand the explanation the book gives\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 #51392 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=51392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. First complete the square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x%5E2-10x%2B3 ALIGN=MIDDLE  ALT=\"y=5x%5E2-10x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3=5x%5E2-10x ALIGN=MIDDLE  ALT=\"y-3=5x%5E2-10x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-3%2B5=5%28x%5E2-2x%2B1%29 ALIGN=MIDDLE  ALT=\"y-3%2B5=5%28x%5E2-2x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 5(-2/2)^2 to both sides to complete the square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2=5%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B2=5%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >Factor the right side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%28x-1%29%5E2-2 ALIGN=MIDDLE  ALT=\"y=5%28x-1%29%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >There's the completed square.<BR>\n" );
document.write( "In the basic equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >} h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. So in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%28x-1%29%5E2-2 ALIGN=MIDDLE  ALT=\"y=5%28x-1%29%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > the vertex is (1,-2) you can verify this by graphing<BR>\n" );
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document.write( "b. The axis of symmetry is at the vertex, so the axis of symmetry is x=1<BR>\n" );
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document.write( "c. The min or max of any quadratic is always at the vertex. So in this case the min is at (1,-2) (the min is the lowest point on the curve)<BR>\n" );
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document.write( "d. The range is all of the outputs of the function (or all the y-values). So the range is all the y's from -2 to infinity or could be written as [-2,infinity)<BR>\n" );
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document.write( "e. Both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%28x-1%29%5E2-2 ALIGN=MIDDLE  ALT=\"y=5%28x-1%29%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5x%5E2-10x%2B3 ALIGN=MIDDLE  ALT=\"y=5x%5E2-10x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > have the same graphs (because they are equivalent)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+5x%5E2-10x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+5x%5E2-10x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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