Find Decreasing Intervals for y = -3x² + 12x - 9

To find the intervals where the function $y = -3x^2 + 12x - 9$ is decreasing, we begin by calculating the derivative:

The derivative of the function is $y' = \frac{d}{dx}(-3x^2 + 12x - 9) = -6x + 12$.

Next, find the critical point using the vertex formula for the x-coordinate, given by:

$x = -\frac{b}{2a} = -\frac{12}{2(-3)} = 2$.

This critical point $x = 2$ is where the derivative changes sign.

Now, we analyze the sign of the derivative $y' = -6x + 12$:

• For $x < 2$, say $x = 0$: $y' = -6(0) + 12 = 12$ (positive).

• For $x > 2$, say $x = 3$: $y' = -6(3) + 12 = -18 + 12 = -6$ (negative).

Therefore, the function is decreasing on the interval $x > 2$.