Finding minimum and maximum values :

To find the maximum or minimum value of a quadratic function, by completing the square of the quadratic function.

Rewrite the function in standard form,

i.e, .

So, the vertex of the graph of f is , which implies the following.

Minimum and maximum values of quadratic functions

Consider the function with vertex .

1. If , f has a minimum at .The minimum value is .

2. If , f has a maximum at .The maximum value is .

The function is .

Compare the above function with .

Rewrite the function in standard form .

.

So, the vertex of the graph of f is

Vertex = = .

  , so, f has a minimum at .The minimum value is .

Therefore, the minimum value is .

We know that domain of the function is all possible x  values and range is all possible y  values.

Therefore,

Domain of the function is all real numbers.

In the minimum point . so the graph of the function cannot be lower than .

Range of the function is  {y |y  ≥ - 25 / 4}.