document.write( "Question 698656: I am unsure of how to do this question. \r
\n" ); document.write( "\n" ); document.write( "Algebraically determine the vertex of the parabola from the standard form (y= -6x^2 + 48x + 9) of the function using another method. \r
\n" ); document.write( "\n" ); document.write( "The first part of the question was to change it to vertex form using completing the square, I did that but I'm not sure what to do above. \n" ); document.write( "
Algebra.Com's Answer #430915 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
the standard form \"y=+-6x%5E2+%2B+48x+%2B+9\"\r
\n" ); document.write( "\n" ); document.write( "change it to vertex form using completing the square\r
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Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

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\n" ); document.write( " \"y=-6+x%5E2%2B48+x%2B9\" Start with the given equation
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\n" ); document.write( " \"y-9=-6+x%5E2%2B48+x\" Subtract \"9\" from both sides
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\n" ); document.write( " \"y-9=-6%28x%5E2-8x%29\" Factor out the leading coefficient \"-6\"
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\n" ); document.write( " Take half of the x coefficient \"-8\" to get \"-4\" (ie \"%281%2F2%29%28-8%29=-4\").
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\n" ); document.write( " Now square \"-4\" to get \"16\" (ie \"%28-4%29%5E2=%28-4%29%28-4%29=16\")
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\n" ); document.write( " \"y-9=-6%28x%5E2-8x%2B16-16%29\" Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of \"16\" does not change the equation
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\n" ); document.write( " \"y-9=-6%28%28x-4%29%5E2-16%29\" Now factor \"x%5E2-8x%2B16\" to get \"%28x-4%29%5E2\"
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\n" ); document.write( " \"y-9=-6%28x-4%29%5E2%2B6%2816%29\" Distribute
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\n" ); document.write( " \"y-9=-6%28x-4%29%5E2%2B96\" Multiply
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\n" ); document.write( " \"y=-6%28x-4%29%5E2%2B96%2B9\" Now add \"9\" to both sides to isolate y
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\n" ); document.write( " \"y=-6%28x-4%29%5E2%2B105\" Combine like terms
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\n" ); document.write( " Now the quadratic is in vertex form \"y=a%28x-h%29%5E2%2Bk\" where \"a=-6\", \"h=4\", and \"k=105\". Remember (h,k) is the vertex and \"a\" is the stretch/compression factor.
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\n" ); document.write( " Check:
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\n" ); document.write( " Notice if we graph the original equation \"y=-6x%5E2%2B48x%2B9\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-6x%5E2%2B48x%2B9%29\" Graph of \"y=-6x%5E2%2B48x%2B9\". Notice how the vertex is (\"4\",\"105\").
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\n" ); document.write( " Notice if we graph the final equation \"y=-6%28x-4%29%5E2%2B105\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-6%28x-4%29%5E2%2B105%29\" Graph of \"y=-6%28x-4%29%5E2%2B105\". Notice how the vertex is also (\"4\",\"105\").
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\n" ); document.write( " So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.
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\n" ); document.write( "\n" ); document.write( "the vertex of the parabola is at (\"4\",\"105\")\r
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\n" ); document.write( "\n" ); document.write( "here is better graph\r
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\n" ); document.write( "\n" ); document.write( "\"+graph%28+600%2C600%2C+-6%2C+10%2C+-5%2C+120%2C+-6x%5E2+%2B+48x+%2B+9%29+\" \n" ); document.write( "
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