Prove linear programming is a special case of quadratic programming

Question

If quadratic programming (QP) encompasses linear programming (LP) for optimization problems, so that every LP is a QP, how can this fact be proven/derived mathematically (elimination or otherwise) from the following quadratic function?

$$f(x) = \frac{1}{2}x^{\text{T}}Ax + c^{\text{T}}x + d$$

And with the reformulation, can a QP solver still be applied to the LP problem?

Answer 1

Choose $A$ as the zero matrix. Then $f(x)=c^tx+d$ is a linear objective function.