document.write( "Question 1040891: If $s$ is a real number, then what is the smallest possible value of $2s^2 - 8s + 19$? \n" ); document.write( "

Algebra.Com's Answer #655834 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "If s is a real number, then what is the smallest possible value of 2s^2 - 8s + 19?
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document.write( "1.  Firmly memorize this:\r\n" );
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document.write( "    A quadratic function  y =   has a minimum/maximum at  x = .     (1)\r\n" );
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document.write( "    To find this maximum/minimum value, substitute  x =   into the quadratic function. \r\n" );
document.write( "    Then min/max, after calculations, is  .                              (2)\r\n" );
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document.write( "    Next,  if  a > 0  then the parabola is open up and the min/max is the minimum.\r\n" );
document.write( "           If  a < 0  then the parabola is open down and the min/max is the maximum.\r\n" );
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document.write( "2.  In your case,  the minimum is at s =  = 2.\r\n" );
document.write( "    To calculate , substitute s = 2 into the quadratic function.  It will produce the same value as (2), but the calculations are easier.\r\n" );
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document.write( "     =  = 8 - 16 + 19 = 11.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lesson Who is who in quadratic equations in this site.\r
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document.write( "Next, memorize this:\r\n" );
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document.write( "     It doesn't matter which letter of the English alphabet is used in the parabola equation as a variable. \r\n" );
document.write( "     To find a min/max and a vertex coordinates, always use the formula (1). It works ALWAYS.\r\n" );
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document.write( "     After finding x, calculate the value of a min/max by substituting the found value  of \"x\" into the parabola equation.\r\n" );
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\n" ); document.write( "And the last notice.\r
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\n" ); document.write( "\n" ); document.write( "There is no need to use so many symbols \"$\" as you do.
\n" ); document.write( "We understand clearly your formulas without it.\r
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