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There is no quadratic equation that is 'linear'. There are linear equations and quadratic equations. Linear equations are equations in which the degree of the variable is 1, and quadratic equations are those equations in which the degree of the variable is 2.
There are many equations that are neither linear nor quadratic. A simple example is a cubic equation, such as y = x3, or a logarithmic equation, such as y = ln(x).
A linear equation has the form of mx + b, while a quadratic equation's form is ax2+bx+c. Also, a linear equation's graph forms a line, while a quadratic equation's graph forms a parabola.
Both are polynomials. They are continuous and are differentiable.
All linear equations are functions but not all functions are linear equations.