Y=x^2+16x+71 equation for parabola

To conver to vertex form, complete the square
y=a(x-h)^2+k
vertex is (h,k)

y=x^2+16x+71
y=(x^2+16x)+71
16/2=8, 8^2=64
y=(x^2+16x+64-64)+71
y=((x+8)^2-64)+71
y=(x+8)^2-64+71
y=1(x+8)^2+7
vertex=(-8,7)

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.