document.write( "Question 586056: How do you find the vertex of this equation? x^2+3x-4? \n" ); document.write( "

Algebra.Com's Answer #373594 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2%2B3x-4\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( "Take half of the $\"x\"$ coefficient $\"3\"$ to get $\"3%2F2\"$ . In other words, $\"%281%2F2%29%283%29=3%2F2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now square $\"3%2F2\"$ to get $\"9%2F4\"$ . In other words, $\"%283%2F2%29%5E2=%283%2F2%29%283%2F2%29=9%2F4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B3x%2Bhighlight%289%2F4-9%2F4%29-4\"$ Now add and subtract $\"9%2F4\"$ . Make sure to place this after the \"x\" term. Notice how $\"9%2F4-9%2F4=0\"$ . So the expression is not changed.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B3x%2B9%2F4%29-9%2F4-4\"$ Group the first three terms.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B3%2F2%29%5E2-9%2F4-4\"$ Factor $\"x%5E2%2B3x%2B9%2F4\"$ to get $\"%28x%2B3%2F2%29%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B3%2F2%29%5E2-25%2F4\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So after completing the square, $\"x%5E2%2B3x-4\"$ transforms to $\"%28x%2B3%2F2%29%5E2-25%2F4\"$ . So $\"x%5E2%2B3x-4=%28x%2B3%2F2%29%5E2-25%2F4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So $\"y=x%5E2%2B3x-4\"$ is equivalent to $\"y=%28x%2B3%2F2%29%5E2-25%2F4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So the equation $\"y=%28x%2B3%2F2%29%5E2-25%2F4\"$ is now in vertex form $\"y=a%28x-h%29%5E2%2Bk\"$ where $\"a=1\"$ , $\"h=-3%2F2\"$ , and $\"k=-25%2F4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Remember, the vertex of $\"y=a%28x-h%29%5E2%2Bk\"$ is (h,k).\r
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\n" ); document.write( "\n" ); document.write( "So the vertex of $\"y=%28x%2B3%2F2%29%5E2-25%2F4\"$ is (-3/2,-25/4). \r
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\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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