Problem: The value of x2−6x+13x^{2}-6 x+13x2−6x+13 can never be less than:
Answer Choices:
A. 444
B. 4.54.54.5
C. 555
D. 777
E. 131313 Solution:
x2−6x+13=(x−3)2+4x^{2}-6 x+13=(x-3)^{2}+4x2−6x+13=(x−3)2+4. The smallest value for this expression, 444 , is obtained when x=3x=3x=3.
or
Graph y=x2−6x+3y=x^{2}-6 x+3y=x2−6x+3. The turning point, whose ordinate is 444 , is a minimum point.