For this case we have the following function:

We apply the following function transformation:
Horizontal translations:
Suppose that h> 0
To graph y = f (x + h), move the graph of h units to the left.
We have then for h = 1:

Rewriting we have:

Rewriting we have:

Answer:
The resulting function when f (x) is shifted to the left 1 unit is:

A quadratic equation refers to an equation with the highest degree of 2. The first equation, 2(x+5)^2 + 8x + 5 + 6 = 0 is the only one with the highest degree of 2 (in (x+5)^2), so that is the quadratic.