The quadratic function depends on the real parameter .

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The quadratic function

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

depends on the real parameter

m

. (i) Find the minimum value of

q(x)

in terms of

m

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

m

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

m

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

q(x)

attains its minimum.