Question

6) Ethan uses the function f(x) = 2x2 + 2x + 4 to track the temperature of a substance over 8 hours. You know that f(3) = 28 meaning that the temperature of the substance is 28°C when you plug in a 3 for x. What is the domain of Ethan’s function?

Answer 1

You have the quadratic function $f(x)=2 x^{2} +2x+4$, 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 $a x^{2} +bx+c$.
In interval notation the domain of the function $f(x)=2 x^{2} +2x+4$ is
(-∞, ∞)