How to fit a non-linear effect during a full factorial design?

[#1]

Dear JMP community,

Can you observe non-linear effects in a full factorial design?

After analyses, a value ( AGC%) was found to have no significant influence on a Y variable (Total number of features).

After maximising desirability, a value of 1000 was recommended for AGC.

However, when I look at the points and plot them on a curve, they come close to a quadratic effect (which could lead to the non-significant influence on that Y variable when assuming it is a linear effect). This has also an effect on the outcome, as based on the points at the curve, I would not select 1000% but a value between 400-600% for AGC target. 

Now my question is whether these quadratic effects can also be represented in a full factorial design or other screening designs, so that they can be taken into account when calculating the significance and illustrating the desirability?

Thanks in advance! 

Extra information: 

[#2]

Most model selection criteria and effect tests would vote in favor of the non-linear model as depicted by your plots. 

Full factorial designs mean that you have included runs representing all possible combinations of all the factor levels. Your X has five levels; there is no other factor.