document.write( "Question 335917: How do I find the vertex and y-intercept of \r
\n" ); document.write( "\n" ); document.write( "y = x² + 8x + 11, \r
\n" ); document.write( "\n" ); document.write( "and how do I write it in standard form?
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Algebra.Com's Answer #240907 by Edwin McCravy(20055) $\"\"$ $\"About$

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How do I find the vertex and y-intercept of \r
\n" ); document.write( "\n" ); document.write( "y = x² + 8x + 11, \r
\n" ); document.write( "\n" ); document.write( "and how do I write it in standard form?
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document.write( "y = x² + 8x + 11\r\n" );
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document.write( "To the side, multiply the 8 by , getting 4\r\n" );
document.write( "Square the 4, getting 16\r\n" );
document.write( "Add 16 to both sides of the equation:\r\n" );
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document.write( "y + 16 = x² + 8x + 11 + 16 \r\n" );
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document.write( "Don't add the 11 and the 16 on the right, instead swap them:\r\n" );
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document.write( "y + 16 = x² + 8x + 16 + 11\r\n" );
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document.write( "Factor the first three terms on the left \r\n" );
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document.write( "y + 16 = (x + 4)(x + 4) + 11\r\n" );
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document.write( "Write the factorization as a square:\r\n" );
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document.write( "y + 16 = (x + 4)² + 11 \r\n" );
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document.write( "Add -16 to both sides:\r\n" );
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document.write( "     y = (x + 4)² - 5\r\n" );
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document.write( "Stick a 1 in front of the parentheses:\r\n" );
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document.write( "     y = 1(x + 4)² - 5\r\n" );
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document.write( "That's the standard form. Compare to\r\n" );
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document.write( "     y = a(x - h)² + k\r\n" );
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document.write( "where (h,k) is the vertex.  So\r\n" );
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document.write( "h=-4 and k=-5 and we have that\r\n" );
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document.write( "(h,k) = (-4,-5) is the vertex.\r\n" );
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document.write( "The y-intercept is found by substituting\r\n" );
document.write( "0 for x:\r\n" );
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document.write( "     y = (x + 4)² - 5\r\n" );
document.write( "     y = (0 + 4)² - 5\r\n" );
document.write( "     y = 4² - 5\r\n" );
document.write( "     y = 16 - 5\r\n" );
document.write( "     y = 11\r\n" );
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document.write( "So the y-intercept is (0,11)\r\n" );
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document.write( "     \r\n" );
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document.write( "Edwin

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