Both are polynomials. They are continuous and are differentiable.
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A linear function is a line where a quadratic function is a curve. In general, y=mx+b is linear and y=ax^2+bx+c is quadratic.
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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.
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.
A linear function is called "linear" because it represents a straight line. To graph a linear function, find two points that satisify that function, plot them, and then draw a straight line between them.