document.write( "Question 102: 1. let f be a quadratic function with a minimum value of -22100, a line of symmetry of x=140, and a y-intercept of (0,-2500).\r
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Algebra.Com's Answer #101 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
1. let f be a quadratic function with a minimum value of
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document.write( "-22100, a line of symmetry of x=140, and a y-intercept of
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document.write( "(0,-2500).
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document.write( "2. the function g is the same as f but relfected about the
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document.write( "x-axis and reduced by a factor of 200.
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document.write( "3. if x equals your grade, what is the value of g to one decimal place?\r
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document.write( ">>...1. let f be a quadratic function...<<\r
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document.write( "f(x) = a(x-h)² + k\r
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document.write( ">>...with a minimum value of -22100,...<<\r
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document.write( "That tells us k = -22100, a > 0\r
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document.write( "So far we have\r
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document.write( "f(x) = a(x-h)² - 22100\r
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document.write( ">>...a line of symmetry of x=140, \r
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document.write( "That tells us h = 140. So far we have\r
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document.write( "f(x) = a(x-140)² - 22100\r
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document.write( ">>...and a y-intercept of (0,-2500)...<<\r
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document.write( "That tells us f(0) = -2500. Substituting\r
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document.write( "-2500 = a(0-140)² - 22100 \r
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document.write( "19600 = 19600a\r
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document.write( "a = 1\r
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document.write( "So we now have\r
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document.write( "f(x) = 1(x-140)² - 22100\r
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document.write( "f(x) = (x-140)² - 22100\r
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document.write( "\n" );
document.write( ">>...2. the function g is the same as f but reflected about the
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document.write( "x-axis...<<\r
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document.write( "To reflect f(x) across the x-axis we multiply the right side
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document.write( "of its equation by -1\r
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document.write( "So far we have for the right side of g(x)\r
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document.write( "-[(x-140)² - 22100]\r
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document.write( "-(x-140)² + 22100 \r
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document.write( ">>...and reduced by a factor of 200...<<\r
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document.write( "That means to form the right side of g(x) we need to
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document.write( "multiply it by 1/200, or divide by 200:\r
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document.write( "[-(x-140)² + 22100]/200 or\r
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document.write( "-x²/200 + 7x/5 + 25/2\r
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document.write( "or\r
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document.write( "g(x) = -.005x² + 1.4x + 12.5\r
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document.write( ">>...3. if x equals your grade, what is the value of g to one
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document.write( "decimal place?...<<
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document.write( "You have to be given your grade.  Apparently this is a
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document.write( "teacher's function for curving grades.  Make a table of
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document.write( "values of possible grades, by substituting these values
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document.write( "of possible grades:  
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document.write( "If your grade is        Your curved grade is 
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document.write( "       x             g(x) = -.005x² + 1.4x + 12.5
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document.write( "      100            g(100) = 102.5
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document.write( "       90             g(90) = 98
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document.write( "       80             g(80) = 92.5
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document.write( "       70             g(70) = 86
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document.write( "       60             g(60) = 78.5
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document.write( "       50             g(50) = 70
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document.write( "       40             g(40) = 60.5
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document.write( "       30             g(30) = 50
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document.write( "       20             g(20) = 38.5
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document.write( "       10             g(10) = 26
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document.write( "        0              g(0) = 12.5        
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document.write( "If your grade is between two of these values, simply substitute
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document.write( "it for x in g(x) = -.005x² + 1.4x + 12.5 to get your curved grade.  \r
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document.write( "Edwin\r
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