Answer
(a) $d(x)= \sqrt {x^4-15x^2+64}$
(b) $d(0)= 8$
(c) $d(1)= \sqrt {50}\approx7.07$
(d) See graph.
(e) $x=\pm2.74$
Work Step by Step
(a) $d(x)=\sqrt {x^2+y^2}=\sqrt {x^2+(x^2-8)^2}=\sqrt {x^4-15x^2+64}$
(b) $d(0)=\sqrt {0^4-15(0)^2+64}=8$
(c) $d(1)=\sqrt {1^4-15(1)^2+64}=\sqrt {50}\approx7.07$
(d) See graph.
(e) Minima of $d(x)$ at $x=\pm2.74$
