For , define…

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

For

m\in\mathbb R

, define

h_m(x)=x^{2}+2(m-1)x+m^{2}-4m+3

. (i) Find the minimum value of

h_m

in terms of

m

. (ii) Hence, find all real values of

m

for which the range of

h_m

[2,\infty)