Determine the maximum or minimum, as well as the domain and range, of the function:
\[ y = x^2 - 4x + 4 \]
Answer (2)
0\ then\ minimum:\\\\\frac{-b}{2a}=\frac{-(-4)}{2\cdot1}=\frac{4}{2}=2\\\\y_{min}=2^2-4\cdot2+4=4-8+4=0\\\\\\domain:x\in\mathbb{R}\\\\\\range:y\in\left<0;\ \infty\right)"> y = x 2 − 4 x + 4 a = 1 ; b = − 4 ; c = 4 a > 0 t h e n minim u m : 2 a − b = 2 ⋅ 1 − ( − 4 ) = 2 4 = 2 y min = 2 2 − 4 ⋅ 2 + 4 = 4 − 8 + 4 = 0 d o main : x ∈ R r an g e : y ∈ ⟨ 0 ; ∞ )
The function y = x 2 − 4 x + 4 has a minimum value of 0 at x = 2 . The domain is all real numbers x ∈ R , and the range is y ∈ [ 0 , ∞ ) .
;
