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## Homework Statement

Let [tex]A[/tex] be a positive definite [tex]n\times n[/tex] real matrix, [tex]b\in\mathbb{R}^n[/tex], and consider the quadratic polynomial [tex]Q(x)=\frac{1}{2}\langle{x, Ax\rangle}-\langle{b, x\rangle}[/tex]. Show that [tex]Q[/tex] is bounded below.

**2. The attempt at a solution**

I have to come up with a constant [tex]m[/tex] so that [tex]Q(x)\ge m[/tex] for all [tex]x\in\mathbb{R}^n.[/tex] I see that [tex]Q[/tex] looks a lot like a parabola. I know how to find the lower bound of a parabola opening upward but I don't know how to generalize this to quadratic forms.

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