Answer
(a) $d(x) =\sqrt {x^4-13x^2+49}$
(b) $d(0) =7$
(c) $d(-1) =\sqrt {37}\approx6.08$
(d) See graph.
(e) $x=\pm2.55$
Work Step by Step
(a) $d(x)=\sqrt {(x-0)^2+(y+1)^2}=\sqrt {x^2+(x^2-7)^2}=\sqrt {x^4-13x^2+49}$
(b) $d(0)=\sqrt {0^4-13(0)^2+49}=7$
(c) $d(-1)=\sqrt {(-1)^4-13(-1)^2+49}=\sqrt {37}\approx6.08$
(d) See graph.
(e) Minima of $d(x)$ at $x=\pm2.55$
