Question 677758
The vertex of y = 6x^2 +3 is (0,3). The min is y = 3 because this is the y coordinate of the vertex and the leading coefficient is positive.


Domain: The set of all real numbers (this is true for any polynomial)


Range: The set of all real numbers such that {{{y>=3}}} (this is because the min is y = 3). Basically any number greater than or equal to 3 is part of the range.


In interval notation, 


Domain: <img src="http://latex.codecogs.com/gif.latex?\large \left(-\infty,\infty\right)" title="x" />


Range: <img src="http://latex.codecogs.com/gif.latex?\large [3,\infty)" title="x" />