Answer
a.
The minimum point is $(-3,685).$
b.
Domain: $(-\infty,\infty)$
Range: $(685,\infty)$
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.
$a = 2 > 0$,
so $f$ has a minimum that occurs at $x=-\displaystyle \frac{b}{2a}$
$-\displaystyle \frac{b}{2a}=-\frac{12}{2(2)}=-3,\quad $
$f(3)=2(-3)^{2}+12(-3)+703=18-36+703=685$
The minimum point is $(-3,685).$
b.
f(x) is defined all real numbers.
f(x) has minimum value $685$ no maximum.
Domain: $(-\infty,\infty)$
Range: $(685,\infty)$
a.
The minimum point is $(-3,685).$
b.
Domain: $(-\infty,\infty)$
Range: $(685,\infty)$