1. **State the problem:** Simplify the expression $ (6 - 7x + x^2) + (6x - 6x^2 + 10) $. 2. **Write down the expression:** $$ 6 - 7x + x^2 + 6x - 6x^2 + 10 $$ 3. **Group like terms:** - Constant terms: $6 + 10$ - $x$ terms: $-7x + 6x$ - $x^2$ terms: $x^2 - 6x^2$ 4. **Simplify each group:** - Constants: $6 + 10 = 16$ - $x$ terms: $-7x + 6x = -x$ - $x^2$ terms: $1x^2 - 6x^2 = -5x^2$ 5. **Write the simplified expression:** $$ 16 - x - 5x^2 $$ 6. **Final answer:** The simplified form of the expression is $16 - x - 5x^2$. This expression is a quadratic polynomial with a negative leading coefficient, so its graph is a downward-opening parabola.