## College Algebra (6th Edition)

a. The maximum point is $(7,-57).$ b. Domain: $(-\infty,\infty)$ Range: $(-57,\infty)$
See p.337. Consider the quadratic function $f(x)=ax^{2}+bx+c$. 1. If $a > 0$, then $f$ has a minimum that occurs at $x=-\displaystyle \frac{b}{2a}$ . This minimum value is $f$($-\displaystyle \frac{b}{2a}$). 2. If $a < 0$, then $f$ has a maximum that occurs at $x=-\displaystyle \frac{b}{2a}$. This maximum value is $f$($-\displaystyle \frac{b}{2a}$) -------------------------- a. $a = -1 < 0$, so $f$ has a maximum that occurs at $x=-\displaystyle \frac{b}{2a}$. $-\displaystyle \frac{b}{2a}=-\frac{14}{2(-1)}=7,\quad$ $f(7)=-7^{2}+14(7)-106=-49+98-106=-57$ The maximum point is $(7,-57).$ b. f(x) is defined all real numbers. f(x) has maximum value $-57$, no minimum. Domain: $(-\infty,\infty)$ Range: $(-57,\infty)$