Sum of Squares of Quadratic Roots

Consider the quadratic equation given by:

$$2x^2 - 8x + 6 = 0$$

In addition to the roots of the equation, we are interested in finding their sum and product. Furthermore, we need to express the sum of the squares of the roots using these derived quantities.

Using Vieta's formulas, if the roots of the equation are denoted as $r_1$ and $r_2$, find the value of $$r_1^2 + r_2^2.$$ Please represent your final answer as a grid-in response.