# Does scatterplot matrix “work” with quadratic variables?

basically I want to plot a scatterplot matrix using a few variables. For simplicity lets say my model is: $$z=\alpha_0 + \alpha_1w+\alpha_2x+\alpha_3y+\alpha_4y^2 + \epsilon$$ When I plot the matrix, I got that all of the explanatory variables exhibit a (strong) positive relationship to the response variable.

Also, given the data, I regress the variables, and eliminated some irrelevant variables. I got that w is irrelevant, and the end regression is: $$z=0.98234+1.02852x+0.38271y-0.83721y^2+\epsilon$$ I know that this end regression is right, because $y^2$ is supposed to have a negative relationship with the response variable however why does the scatterplot matrix fail to capture this?

One set of data could have $y=100 + 0.01x$ and have a very strong positive correlation (most of the data on the line).
A second set of data could have $y=100 + 20x$ and have a very weak positive correlation (data scattered widely either side of the line).