You have the quadratic function [tex]f(x)=2 x^{2} +2x+4[/tex], and remember that all quadratic functions are parabolas opening at point called the vertex. Since you can plug any real number in our parabola here, its domain is all the real numbers, and this is true for all the quadratic functions of the form [tex]a x^{2} +bx+c[/tex].
In interval notation the domain of the function [tex]f(x)=2 x^{2} +2x+4[/tex] is
(-∞, ∞)
