what is the domain and range of the quadratic function g(x) =x^2-x-6

Question

what are the reasonable domain and range of the quadratic function

Answer 1

The domain of a quadratic function is all real numbers.

 

To find the range, we need to find the vertex of the quadratic function.

 

x-coodinate of the vertex can be found using          x=-b/(2a)

 

where:

a = 1

b = -1

 

x = -(-1) / (2*1)

x = 1 / 2

 

 

Evaluate g(1/2) to find the y-coordinate of the vertex.

 

g(1/2) = (1/2)² - (1/2) - 6

 

          = (1/4) - (1/2) - 6

 

          = -6.25

 

The vertex is (0.5, -6.25).  Since the quadratic function represents a parabola that opens upward, the range is   (-6.25, ∞).