document.write( "Question 148665: Hello. Please and I mean Please, help me know how to find the y value in a parabola. The y value should either be the highest or the lowest point in a positive or negative curved u. Thank you very much for your time in helping me solve this question. \n" ); document.write( "
Algebra.Com's Answer #109005 by Edwin McCravy(20055)\"\" \"About 
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Hello. Please and I mean Please, help me know how to find the y value in a parabola. The y value should either be the highest or the lowest point in a positive or negative curved u. Thank you very much for your time in helping me solve this question. \r
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document.write( "The formula for the vertex of a parabola, which\r\n" );
document.write( "is the highest or lowest point, whose equation is:\r\n" );
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document.write( "\"y+=+Ax%5E2%2BBx%2BC\"\r\n" );
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document.write( "First we calculate the discriminant\r\n" );
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document.write( "\"D=B%5E2-4AC\".\r\n" );
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document.write( "then the vertex is\r\n" );
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document.write( "(\"-B%2F%282A%29\", \"-D%2F%284A%29\") \r\n" );
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document.write( "Example:\r\n" );
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document.write( "For the parabola \r\n" );
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document.write( "\"y+=+-x%5E2%2B2x%2B8\"\r\n" );
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document.write( "We can find a few points by selecting\r\n" );
document.write( "arbitrary values for x, substituting\r\n" );
document.write( "and finding the y-values.\r\n" );
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document.write( "For example, if we substitute \"x=-1\"\r\n" );
document.write( "into\r\n" );
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document.write( "\"y+=+-x%5E2%2B2x%2B8\"\r\n" );
document.write( "\"y+=+-%28-1%29%5E2%2B2%28-1%29%2B8\"\r\n" );
document.write( "\"y+=+-1-2%2B8\"\r\n" );
document.write( "\"y+=+5\"\r\n" );
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document.write( "So we have the point (-1,5)\r\n" );
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document.write( "We can find others the same way.\r\n" );
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document.write( "I found (-3,-7), (-1,5), (0,8), (3,5), and (5,-7).\r\n" );
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document.write( "Let's plot those:\r\n" );
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document.write( "We compare this problem:\r\n" );
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document.write( "\"y+=+-x%5E2%2B2x%2B8\"\r\n" );
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document.write( "to\r\n" );
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document.write( "\"y+=+Ax%5E2%2BBx%2BC\"\r\n" );
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document.write( "and find \"A=-1\", \"B=2\", \"C=8\"\r\n" );
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document.write( "To find the vertex, we first calculate the discriminant\r\n" );
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document.write( "\"D=B%5E2-4AC=%282%29%5E2-4%28-1%29%288%29+=+4%2B32=36\".\r\n" );
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document.write( "then the vertex is\r\n" );
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document.write( "(\"-B%2F%282A%29\", \"-D%2F%284A%29\") =\r\n" );
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document.write( "(\"-%282%29%2F%282%28-1%29%29\", \"-%2836%29%2F%284%28-1%29%29\") =\r\n" );
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document.write( "(\"-2%2F%28-2%29\", \"-%2836%29%2F%28-4%29\") =\r\n" );
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document.write( "(\"1\", \"9\") =\r\n" );
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document.write( "So we plot the vertex at (\"1\", \"9\")\r\n" );
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document.write( "and sketch in the parabola:\r\n" );
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document.write( "Edwin
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