Lösung 2.3:6b
Aus Online Mathematik Brückenkurs 1
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By completing the square, the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value, | By completing the square, the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value, | ||
| + | {{Displayed math||<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}} | ||
| - | + | Because <math>(x-2)^{2}</math> is a quadratic, this term is always larger than or equal to 0 and the whole expression is therefore at least equal to -2, which occurs when <math>x-2=0</math> and the quadratic is zero, i.e. <math>x=2</math>. | |
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| - | Because | + | |
| - | <math> | + | |
| - | is a quadratic, this term is always larger than or equal to | + | |
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| - | and the whole expression is therefore at least equal to | + | |
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| - | and the quadratic is zero, i.e. | + | |
| - | <math>x= | + | |
Version vom 11:34, 29. Sep. 2008
By completing the square, the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value,
Because \displaystyle (x-2)^{2} is a quadratic, this term is always larger than or equal to 0 and the whole expression is therefore at least equal to -2, which occurs when \displaystyle x-2=0 and the quadratic is zero, i.e. \displaystyle x=2.
