Answer
$$\eqalign{
& {\text{Vertices }}\left( { - 2,0} \right){\text{ and }}\left( {2,0} \right) \cr
& {\text{Foci }}\left( { - 2\sqrt 5 ,0} \right){\text{ and }}\left( {2\sqrt 5 ,0} \right) \cr
& {\text{Asymptotes: }}y = 2x{\text{ and }}y = - 2x \cr} $$
Work Step by Step
$$\eqalign{
& 4{x^2} - {y^2} = 16 \cr
& {\text{Divide the equation by 16}} \cr
& \frac{{{x^2}}}{4} - \frac{{{y^2}}}{{16}} = 1 \cr
& {\text{The equation is in the standard form }}\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1.{\text{ Then,}} \cr
& \frac{{{x^2}}}{4} - \frac{{{y^2}}}{{16}} = 1,\,\,\,\,\,a = 2,\,\,\,b = 4 \cr
& c = \sqrt {{a^2} + {b^2}} = \sqrt {{2^2} + {4^2}} = 2\sqrt 5 \cr
& \cr
& {\text{With:}} \cr
& {\text{Vertices }}\left( { - a,0} \right){\text{ and }}\left( {a,0} \right) \cr
& {\text{Vertices }}\left( { - 2,0} \right){\text{ and }}\left( {2,0} \right) \cr
& {\text{Foci }}\left( { - c,0} \right){\text{ and }}\left( {c,0} \right) \cr
& {\text{Foci }}\left( { - 2\sqrt 5 ,0} \right){\text{ and }}\left( {2\sqrt 5 ,0} \right) \cr
& {\text{Asymptotes: }}y = \frac{b}{a}x{\text{ and }}y = - \frac{b}{a}x \cr
& {\text{Asymptotes: }}y = 2x{\text{ and }}y = - 2x \cr
& \cr
& {\text{Graph}} \cr} $$
