Linearity in Linear Regression

A linear regression may have power or degree of feature >1 like ax² + bx+c , but still be a linear regression because when we say linear regression we are looking at linearity of the coefficients/weights associated with the features and not the power or degree of features. In ax²+bx+c -> a,b and c are still linear though the features have higher order ie x² . Simple linear regression with features having power 1 are common, and in such case we find the best fit line. In case of power or degree of feature >1 like ax²+bx+c which has quadratic features (with linear coefficients) the best fit will be a parabola, a curve. It will be called polynomial regression, thought it has linear coefficients and hence a type of linear regression.