Answer
a.
The maximum point is $(7,-57).$
b.
Domain: $(-\infty,\infty)$
Range: $(-57,\infty)$
Work Step by Step
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: $(-57,\infty)$
