can a quadratic function have a constant rate of change?

Question

i need help for my assignment please

Answer 1

Yes it can.  If you pick any point in time and draw a straight line tangent to the curve at that point, you get your constant rate of change.  This is called the derivative.

 

If you do the same thing but using two points in time, you get the secant line. This is called the average rate of change.

Answer 2

No.  The rate of change of a quadratic function is linear.

 

Example:

 

f(x) = ax² + bx + c  (a ≠ 0)

 

The rate of change of f(x) with respect to x is 2ax + b, which is linear, not constant.