1. **Problem:** Express $3 - 12x - 2x^2$ in the form $ax^2 + bx + c$ and find the turning point of the curve $y = 3 - 12x - 2x^2$. 2. **Rewrite the quadratic:** The standard form of a quadratic is $ax^2 + bx + c$. Given expression is $3 - 12x - 2x^2$. 3. **Rearrange terms:** Write in descending powers of $x$: $$y = -2x^2 - 12x + 3$$ So, $a = -2$, $b = -12$, $c = 3$. 4. **Formula for turning point:** The $x$-coordinate of the turning point is given by $$x = -\frac{b}{2a}$$ Substitute $a$ and $b$: $$x = -\frac{-12}{2 \times -2} = -\frac{-12}{-4} = -3$$ 5. **Find $y$-coordinate:** Substitute $x = -3$ into $y = -2x^2 - 12x + 3$: $$y = -2(-3)^2 - 12(-3) + 3 = -2(9) + 36 + 3 = -18 + 36 + 3 = 21$$ 6. **Turning point coordinates:** The turning point is at $(-3, 21)$. --- **Final answer:** The expression in standard form is $y = -2x^2 - 12x + 3$. The turning point of the curve is at $\boxed{(-3, 21)}$.