Because the leading coefficient is positive, we know that the vertex is a minimum.
For a general quadratic function:
y = ax²+ bx+c
The vertex is a:
Maximum if a < 0, this happens because in this case the parabola opens down.
Minimum if a > 0, this happens because in this case the parabola opens up.
Here we have the quadratic:
y = 4x²+ 4x+1
We can see that the leading coefficient is positive, thus, the vertex is a minimum.
Complete question:
"is the vertex a max or min value for the function 4x²+ 4x+1?"