Find the domain of the equation y=5x^2+6x+7

Question

im not sure how to figure this problem out

Answer 1

All polynomials have a domain of all real numbers.  If the function is not a polynomial, then you will have restricted domain.  This is when the vertical asymptotes comes in.  Remember this fact. 

Answer 2

When finding the domain, what you are essentially looking for are what x values you are allowed to use in the equation. So if you had a rational number such as 2/x, x would not be able to equal zero since you are not able to divide anything by zero. Or, if you have a square root, such as sqrt(x), everything inside of the square root must be greater than or equal to zero, or you'll have an imaginary number. Since your equation (y=5x^2+6x+7) does not have anything in which x would be restricted (a rational value or a square root), then you are able to plug in any value into x without breaking the universe. Therefore, your answer is all real numbers.