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A quadratic expression is an algebraic expression having the degree of 2. It is typically an expression in the variable 'x' (or any other variable) having the highest exponent of 2. An example is
x^2 + 2x+ 3
A quadratic equation is an equation in which we equate a quadratic expression with zero. Thus, the following is a quadratic equation:
x^2 + 2x + 3 = 0
A quadratic equation does not have more than two solutions. They are called the roots, zeros or x-intercepts of the quadratic equation.

A quadratic function is the equation of two variables in which the dependent variable is equal to a quadratic expression in the independent variable. For example, in the following equation:
y = x^2 + 2x + 3
the dependent variable is 'y' and it is equal to a quadratic expression in the independent variable 'x'.