Solution 2.3:8c
From Förberedande kurs i matematik 1
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- | {{ | + | By completing the square, we can rewrite the function as |
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- | + | {{Displayed math||<math>f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2,</math>}} | |
- | [[ | + | |
+ | and when the function is written in this way, we see that the graph <math>y = (x-3)^{2} + 2</math> is the same curve as the parabola <math>y=x^{2}</math>, but shifted two units up and three units to the right (see sub-exercise a and b). | ||
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+ | {| align="center" | ||
+ | |align="center"|[[Image:2_3_8_c-1.gif|center]] | ||
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+ | |align="center"|[[Image:2_3_8_c-2.gif|center]] | ||
+ | |- | ||
+ | |align="center"|<small>The graph of ''f''(''x'') = ''x''²</small> | ||
+ | || | ||
+ | |align="center"|<small>The graph of ''f''(''x'') = ''x''² - 6x + 11</small> | ||
+ | |} |
Current revision
By completing the square, we can rewrite the function as
\displaystyle f(x) = x^{2}-6x+11 = (x-3)^{2} - 3^{2} + 11 = (x-3)^{2} + 2, |
and when the function is written in this way, we see that the graph \displaystyle y = (x-3)^{2} + 2 is the same curve as the parabola \displaystyle y=x^{2}, but shifted two units up and three units to the right (see sub-exercise a and b).
The graph of f(x) = x² | The graph of f(x) = x² - 6x + 11 |