document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=734089>Question 734089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complete the square in graphing form: y = x^2 - 7x + 5?\r<BR>\n" );
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document.write( "How to solve this? I think I can used the quadratic formula to solve it but I'm a bit confused. I think there are a few ways to solve this. I searched and found this on Yahoo.\r<BR>\n" );
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document.write( "http://answers.yahoo.com/question/index?qid=20090806151908AAkOA70\r<BR>\n" );
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document.write( "I followed these step by step from this person. It still confuses me and I think this person made a mistake too. Here is what I got so far with mine just by following this person's step by step tips.\r<BR>\n" );
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document.write( "y = x^2 - 7x + 5\r<BR>\n" );
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document.write( "I moved the 5 over to the other side like he did and got this. Moving it would make turn it into a negative number.\r<BR>\n" );
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document.write( "y - 5 = x^2 - 7x\r<BR>\n" );
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document.write( "Now to take 7 divide that in half which give us 3.5<BR>\n" );
document.write( "Now we take that and square root it. It comes out to be 12.25<BR>\n" );
document.write( "So now we are here.\r<BR>\n" );
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document.write( "y - 5 + 12.25 = x^2 - 7x + 12.25\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "y + 7.25 = x^2 - 7x + 12.25\r<BR>\n" );
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document.write( "and following the steps that turns out to be this.\r<BR>\n" );
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document.write( "y + 7.25 = (x-3.5)^2\r<BR>\n" );
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document.write( "This is where I get all confused from this point on. I learned from asking on Yahoo that the 12.25 remaining on the right side is not needed. I can just dropped that. Now I have to move the 7.25 from the left side, which used to be a -5, to the right side again. As before when I changed the 5 to a -5 when I moved it from the right to the left, do I change it again as I move it to the right?\r<BR>\n" );
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document.write( "It should end up being this.\r<BR>\n" );
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document.write( "y = (x-3.5)^2 - 7.25\r<BR>\n" );
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document.write( "Right? More confused now. Following his steps on Yahoo, I found out that the Vertex is (3.5, -7.25). I'm guessing the -3.5 in the equation changes into a positive and the -7.25 stay the same. How do I graph it and how do I solve the remaining. I Google the equation and it show me the graph. It's turns out being a U shape on the graph but I don't know where I should put all the points on the line.\r<BR>\n" );
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document.write( "Sun </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448712 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=448712\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Complete the square in graphing form: y = x^2 - 7x + 5?<BR>\n" );
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document.write( "The idea to keep in mind is that the \"vertex form\" of a quadratic is:<BR>\n" );
document.write( "y = a(x – h)^2 + k<BR>\n" );
document.write( "where<BR>\n" );
document.write( "(h,k)is the vertex<BR>\n" );
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document.write( "y = x^2 - 7x + 5<BR>\n" );
document.write( "since the y is already in the correct position, complete the square ONLY on the right side:<BR>\n" );
document.write( "y = x^2 - 7x + 5<BR>\n" );
document.write( "group x's:<BR>\n" );
document.write( "y = (x^2 - 7x) + 5<BR>\n" );
document.write( "add (b/2)^2 to the inside of the () and balance by subtracting on the outside:<BR>\n" );
document.write( "y = (x^2 - 7x+12.25) + 5-12.25<BR>\n" );
document.write( "y = (x-3.5)^2-7.25<BR>\n" );
document.write( "from \"y = a(x – h)^2 + k\"<BR>\n" );
document.write( "we see that the vertex is:<BR>\n" );
document.write( "(3.5, -7.25)<BR>\n" );
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document.write( "First point on the graph (i.e., the lowest point on the graph)<BR>\n" );
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document.write( "To find y-intercepts, set x=0 and solve for y:<BR>\n" );
document.write( "y = (x-3.5)^2-7.25<BR>\n" );
document.write( "y = (0-3.5)^2-7.25<BR>\n" );
document.write( "y = (-3.5)^2-7.25<BR>\n" );
document.write( "y = 12.25-7.25<BR>\n" );
document.write( "y = 4.75<BR>\n" );
document.write( "Second point is at (0, 4.75)<BR>\n" );
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document.write( "To find x-intercepts, set y=0 and solve for x:<BR>\n" );
document.write( "0 = (x-3.5)^2-7.25<BR>\n" );
document.write( "7.25 = (x-3.5)^2<BR>\n" );
document.write( "take the square root of both sides:<BR>\n" );
document.write( "sqrt(7.25) = x-3.5<BR>\n" );
document.write( "+-sqrt(7.25)+3.5 = x<BR>\n" );
document.write( "6.24 = x<BR>\n" );
document.write( "and<BR>\n" );
document.write( "0.81 = x<BR>\n" );
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document.write( "Third point is at (6.24,0)<BR>\n" );
document.write( "Fourth point is at (.81,0)<BR>\n" );
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