Given $\mathrm{f}(x)=x^2-6x+11,$ express $\mathrm{f}(x)$ in completed-square form; state it

Question

Given $\mathrm{f}(x)=x^2-6x+11,$ express $\mathrm{f}(x)$ in completed-square form; state its minimum value and where it occurs; state the turning point and axis of symmetry of $y=\mathrm{f}(x)$.

Accepted Answer

(a) $\mathrm{f}(x)=(x-3)^2+2$; (b) Minimum $2$ at $x=3$; (c) Turning point $(3,2)$; Axis $x=3$.

Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities