Graph the function and state the domain and range?

Question

g(x)=x^2-2x-15

Answer 1

g(x) has a minimum of -16 at x = 1 so range is y=/> -16
The domain is all real numbers since g(x) is a poynomial.
Since x^2 -2x-15 = (x-5)(x+3) the roots are x =5 and x= -3.

The y-intercept is (0,-15)

The curve is a parabola with vertex at (1,-16) and axis of symmetry x=1.

Answer 2

g(x) = x^2 - 2x - 15
=> g(x) = (x - 1)^2 - 16

As g(x) is a polynomial, its domain is R.
- 16 is its minimum value when x - 1 = 0.
So, the range is [-16, ∞).

To plot the graph, note that it is a parabola with vertex
(1, -16), its axis is parallel to y-axis having equation x = 1.
The vertex (1, -16) is the minimum point on it and the maximum value of g(x) tends to ∞.