Mathematics

Problem

The quadratic function

q(x)=x^{2}-4x+m

depends on the real parameter

m

. a. (i) Find the minimum value of

q(x)

in terms of

m

. b. (ii) Determine the set of all real values of

m

for which this minimum value is less than or equal to zero. c. (iii) For each value of

m

obtained in part (ii), state the coordinates of the point at which

q(x)

attains its minimum.