Let's use these characteristics to compare the graphs of a quadratic function and a linear function.

 

Quadratic Function Linear Function

second degree function

Eg.

Parabola

Note: Since a = 0.5 (positive), the parabola opens upward.

two x-intercepts

x = −9, x = −1

  

first degree function

Eg.

Straight line

 

one x-intercept

x = −4.5

domain:
range:

 

  

domain:
range:

The vertex, which corresponds to the location of the minimum, occurs at (−5, −8). (There is a minimum because the graph opens upward.)

 

   no maximum or minimum
The axis of symmetry is located at the midpoint between the x-intercepts of x = −9 and x = −1
x = −5
   no vertical axis of symmetry

Â