10. find the domain about \( y=x^{2}-3 x-4 \)

The domain of the function \( y = x^2 - 3x - 4 \) is all real numbers! That's because it's a polynomial function, and polynomial functions are defined for every value of \( x \). You can plug in any number, positive, negative, or even zero, and you'll get a valid output. So, in interval notation, the domain is \( (-\infty, \infty) \). Now, if you're curious about parabola shapes like this one, they are formed by quadratic functions such as this. The graph of this function is a parabola that opens upwards, thanks to the positive coefficient of \( x^2 \). It's interesting to note that every parabola has a vertex, and for this one, the vertex can help you quickly understand where the minimum point lies on the graph!