Given quadratic function $f : \mathbb{R}^n \to \mathbb{R}$ defined by $f(\mathbf{x})=\mathbf{x}^\top \mathbf{A} \, \mathbf{x}+b$ where the matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ is symmetric and positive definite, and $b \in \mathbb{R}$. How can one prove that the function $f$ is convex?
I know that all eigenvalues of $\mathbf{A}$ are $> 0$ ($\lambda_i>0$) and also $\mathbf{x}^\top \mathbf{A}\,\mathbf{x}>0$ but I don't know how start the proof.