document.write( "Question 32040This question is from textbook College Algebra
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I'm totally stuck!  I've tried working it but I seem to get stuck on the same
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document.write( "spot!  Here's the problem: \r
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document.write( "For the function y = x2 - 4x - 5, perform the following tasks:\r
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document.write( "a) Put the function in the form y = a(x - h)2 + k.\r
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document.write( "b) What is the line of symmetry?
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document.write( "c) Graph the function using the equation in part a.  Explain why it is not
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document.write( "necessary to plot points to graph when using y = a (x – h)2 + k.\r
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document.write( "d) In your own words, describe how this graph compares to the graph of
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document.write( "   y = x2?\r
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document.write( "For \"a\", I got y=(x-2)2 - 14.  From there, I'm totally lost!  Can somebody
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document.write( "help!  (P.S.  I haven't taken algebra since high school and that was 15 yrs
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document.write( "ago!)  :-)_\r
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document.write( "Thanks!
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document.write( "
Algebra.Com's Answer #18547 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
 \"y+=+x%5E2-4x-5\"\r
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document.write( "a) Convert to\"y+=+a%28x-h%29%5E2%2Bk\"form.
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document.write( "\"y+=+x%5E2-4x-5\" Add 5 to both sides.
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document.write( "\"y%2B5+=+x%5E2-4x\" Complete the square in the x-terms by adding the square of half the x-coefficient \"%284%2F2%29%5E2+=+4\"to both sides.
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document.write( "\"y%2B5%2B4+=+x%5E2-4x%2B4\" Factor the right side. Simplify the left side.
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document.write( "\"y%2B9+=+%28x-2%29%5E2\" Finally, subtract 9 from both sides.
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document.write( "\"y+=+%28x-2%29%5E2-9\"
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document.write( "Compare this with \"y+=+a%28x-h%29%5E2%2Bk\"
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document.write( "a = 1, h = 2, and k = -9\r
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document.write( "b) The line of symmetry (LOS) is the vertical line through the center of the vertex. The vertex is located at (h, k), so in this problem, the vertex is located at (2, -9).
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document.write( "The LOS is therefore the vertical line x = 2\r
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document.write( "c)& d) The graph of\"y+=+x%5E2-4x-5\"(in red).
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document.write( "The graph of \"y+=+x%5E2\"(in green).
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document.write( "\"graph%28300%2C200%2C-6%2C6%2C-10%2C5%2Cx%5E2-4x-5%2Cx%5E2%29\"
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document.write( "As you can see, the two parabolas have the same shape but the red one (your equation) is translated to the right by h units (h=2) and down k units (k = -9). So by first graphing the the parabola\"y+=+x%5E2\" whose vertex lies at the origin, then translating (sliding) it so that the vertex is at the location defined by (h, k) in your equation, you really don't need to plot points. \n" );
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