I have a hard time understanding the term 'linear regression'. For what I know, linear means polynomial of degree 1. But then, I found that in one of my lectures, the lecturers are saying that this regression is a linear regression: $$Y_i=\alpha_0+\alpha_1 x_i +\alpha_2 x_i^2$$
How is this a linear regression when it has quadratic terms in it? Does it not make it a non-linear regression? However when there is a quadratic curve as the regression, it is called a non-linear regression. Which is right?