Let's solve the quadratic equation by examining its roots. The given quadratic equation is:
[tex]\[ y = -2x^2 - 8x - 8 \][/tex]
To find the roots, we need to determine the values of [tex]\( x \)[/tex] for which [tex]\( y = 0 \)[/tex]. Essentially, we're solving:
[tex]\[ -2x^2 - 8x - 8 = 0 \][/tex]
After thorough analysis, we find that the solution to this quadratic equation yields one real solution:
[tex]\[ x = -2 \][/tex]
So, the correct answer from the given options is:
[tex]\[ -2 \][/tex]
