document.write( "Question 83113: Rewrite each equation in vertex form. Then sketch the graph.\r
\n" ); document.write( "\n" ); document.write( "19. a. y=4x^2+8x-4\r
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Algebra.Com's Answer #60024 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "a. y=4x^2+8x-4        answer: y = 4(x+1)²-8 \r\n" );
document.write( "b. y=-3x^2-4x-1       answer: y = -3 + \r\n" );
document.write( "c. y=-5x^2+10x+1      answer: y = 5(x-1)²+6  \r\n" );
document.write( "d. y=-2x^2+10x-11     answer: y = -2(x-5/2)²+3/2\r\n" );
document.write( "e. y=3x^2+9x+6        answer: y = -3 - \r\n" );
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document.write( "I'll do (b) only.  The others are the same.\r\n" );
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document.write( " y = -3x² - 4x - 1\r\n" );
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document.write( "Factor the coefficient of x² out of the first two terms.\r\n" );
document.write( "(Do not factor out x with it)\r\n" );
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document.write( "y = -3(x² + x) - 1\r\n" );
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document.write( "To the side multiply  by , getting \r\n" );
document.write( "Square  getting \r\n" );
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document.write( "Add and then subtract  inside the parentheses:\r\n" );
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document.write( "y = -3(x² + x +  - ) - 1\r\n" );
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document.write( "Change the parentheses to brackets so parentheses may be\r\n" );
document.write( "inserted:\r\n" );
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document.write( "y = -3[x² + x +  - ] - 1\r\n" );
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document.write( "Factor the first three terms in the brackets as a perfect\r\n" );
document.write( "square:\r\n" );
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document.write( "y = -3[ - ] - 1\r\n" );
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document.write( "Remove the bracket by distributing the -3, remembering\r\n" );
document.write( "to leave the  intact:\r\n" );
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document.write( "y = -3 +  - 1\r\n" );
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document.write( "Write the 1 as \r\n" );
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document.write( "y = -3 +  - \r\n" );
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document.write( "y = -3 + \r\n" );
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document.write( "Now plot the vertex (,)\r\n" );
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document.write( "Find the x-intercepts by setting y = 0\r\n" );
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document.write( "              y = -3x² - 4x - 1 \r\n" );
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document.write( "              0 = -3x² - 4x - 1\r\n" );
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document.write( "   3x² + 4x + 1 = 0\r\n" );
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document.write( "(3x + 1)(x + 1) = 0\r\n" );
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document.write( "3x + 1 = 0                x + 1 = 0\r\n" );
document.write( "    3x = -1                   x = -1\r\n" );
document.write( "     x = \r\n" );
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document.write( "So the x intercepts are (,0) and (-1,0)\r\n" );
document.write( "Plot them.\r\n" );
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document.write( "Find the y-intercept by letting x = 0 in the original\r\n" );
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document.write( " y = -3x² - 4x - 1\r\n" );
document.write( " y = -3(0)² -4(0) - 1\r\n" );
document.write( " y = 0 - 4 - 1\r\n" );
document.write( " y = -1\r\n" );
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document.write( "So plot the y-intercept (0.-1) too\r\n" );
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document.write( "Now draw a smooth parabola through those 4 points:\r\n" );
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document.write( "Edwin

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