When the lowest point of the first formula is x=-a,
y=a^2-2a^2-( 1-√3)a+√3
=-a^2-( 1-√3)a+√3
=(-a- 1)(a-√3)
If this is less than or equal to zero
Then a & gt=√3 or a < =- 1
The lowest point of the second formula is x=- 1.
y=3a^2- 1
The range less than or equal to zero is
-√ 1/3 & lt; = a & lt=√ 1/3
When a & gt=√3 or a < =- 1 is greater than zero.
So one of these two functions must be above the x axis.