Suppose that $f: \mathbb R^3 →\mathbb R$, where $f$ is defined by $f(x_1, x_2, x_3)=3x_1-2x_3+x_1(2x_2-1)+(x_1+x_2-x_3)^2-1000$

Question

Show that $f$ is a vector quadratic function.

Proof:
From my computations, I have got this

$$f(x_1, x_2, x_3)=x_1^2+x_2^2+x_3^2+2x_1-2x_3+4x_1x_2-2x_2x_3-2x_1x_3-1000$$

But due to $x_1, x_3$ are constant terms. I am unable to show it in form of vector quadratic function.
Any hint???