Question

determine the domain and the range of the function
x^2+6x

Answer 1

domain of any polynomial is all real number

Answer 2

for the range, since this is a parabola that opens up, find the second coordinate of the vertex, that will be the lowest value of the range

Answer 3

first coordinate of the vertex is \(-\frac{b}{2a}\) in your case iti is \(-\frac{6}{2}=-3\)
second coordinate of the vertex is what you get when you replace \(x\) by \(-3\)