Solution 2.3:8c

From Förberedande kurs i matematik 1

By completing the square, we can rewrite the function as

f(x)=x2−6x+11=(x−3)2−32+11=(x−3)2+2

and when the function is written in this way, we see that the graph y=(x−3)2+2 is the same curve as the parabola y=x2, 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