So I think the question is basically asking for the minimum y value you could get from the functions.
For the first function,
[tex]y=4 x^{2} +8x+1[/tex]
to find the minimum y. (Use x=-b/2a to find its vertex)
so in this case a=4 b=8
x=-8/2(4)=-1 the the minimum value will have -1 as its x coordinates,
[tex]y=4(-1)^2+8(-1)+1=4-8+1=-3 [/tex] plug in x=-1 to find y.
(-1,-3) for minimum value for the first function
For the second function,
(-1,0) is the vertex of the function, which is the minimum of the function.
compare the first function with y=-3 and second function y=0.
The first function will have the least minimum value and the coordinates are (-1,-3).
