A linear-quadratic dose response is a relationship between dose and biological response that is curved. This implies that the rate of change in response is different at different doses. The response may change slowly at low doses, for example, but rapidly at high doses. A linear-quadratic dose response is written mathematically as follows: if Y represents the expected, or average response and D represents dose, then

Y = aD + bD²

where a is the linear coefficient (or slope) and b is the quadratic coefficient (or curvature).

See also Dose response, Threshold dose, and Linear dose response.