Since x is greater than OR equal to 0 and less than OR equal to 4, you use the bracket to indicate the endpoints of the interval [0,4].
Had it been greater than 0 and less than 4, in other words if it did not include the endpoints, the correct notation would be (0,4) with parentheses.
Although the function is a quadratic, and therefore a parabola, the domain coincides with the axis of symmetry, so we know the function is increasing throughout its domain. This means the function will range from its f(0) value and its f(4) value.
f(0) = 3(0)^2 + 8 = 0 + 8 = 8
f(4) = 3(4)^2 + 8 = 48 + 8 = 56
so domain is [0,4] and range is [8,56]
