Given $\mathrm{g}(x)=-2x^2+8x+1,$ complete the square and find its maximum value over all rea

Question

Given $\mathrm{g}(x)=-2x^2+8x+1,$ complete the square and find its maximum value over all real $x$; find the minimum and maximum values of $\mathrm{g}(x)$ when $0\le x\le3$, stating where each occurs.

Accepted Answer

(a) $\mathrm{g}(x)=-2(x-2)^2+9$; Global maximum $9$ at $x=2$; (b) On $[0,3]$, Minimum $1$ at $x=0$, Maximum $9$ at $x=2$.

Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities