Find Decreasing Intervals for y = -4x² - 8x - 12: Quadratic Function Analysis

The function given is $y = -4x^2 - 8x - 12$. To determine where it is decreasing, we first find the vertex:

• The formula for the x-coordinate of the vertex is $x = -\frac{b}{2a}$.
• Substituting the values for $a$ and $b$ yields $x = -\frac{-8}{2 \times -4} = -1$.

Since the coefficient of $x^2$, which is $a = -4$, is negative, the parabola opens downwards. For a downward-opening parabola, the function decreases to the right of the vertex.

Consequently, the interval where the function decreases is $x > -1$.

Therefore, the solution is $x > -1$.