Step-by-step explanation:
the extreme values (minimum, maximum) of a function are the zero points of the first derivation of the function.
so,
f'(x) = 2x + b
and then
2x + b = 0
we know, x = 20 for the minimum
2×20 + b = 0
40 + b = 0
b = -40
therefore, the actual function is
f(x) = x² - 40x + 164
the target format is
f(x) = (x - h)² + k = x² - 2hx + h² + k
so,
-40x = -2hx
-40 = -2h
h = 20
and
h² + k = 164
20² + k = 164
400 + k = 164
k = -236
