prove quadratic equation are continuous in $\mathbb R^n$

prove quadratic equation are continuous in $\mathbb R^n$

$$\text{prove quadratic equation are continuous in }\mathbb{R}^{n}\text{
and }$$
$$\textbf{Q}_A(\vec{v})=\vec{v}^{T}\textbf{A}\vec{v}=\sum_{i}^{n}\sum_{j}^{n}\text{a}_{ij}\text{x}_{i}\text{x}_{j}\quad\text{
such as }\quad \vec{v}\in\mathbb{R}^{n}\text{ and
}\textbf{A}\in\text{Mat}_{n}(\mathbb{R})$$
$\text{We know
}\sum_{i}^{n}\sum_{j}^{n}\text{a}_{ij}\text{x}_{i}\text{x}_{j}\text{ is a
polynomial with respect to } \\x_1\dots x_n \text{ and is continuous on
each }x_i\in\mathbb{R}$ $\text{But how to prove
}\textbf{Q}_{A}(\vec{v})\text{ continuous }\text{ s.t
}\vec{v}\in\mathbb{R}^{n}$