Solution 2.3:6b
From Förberedande kurs i matematik 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, |
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| - | { | + | {{Displayed math||<math>x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}</math>}} |
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| + | 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>. | ||
Current revision
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,
| \displaystyle x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.} |
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.
