As you can see, both curves are upward. Only the lowest point is calculated.

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.