We are given the equation $y = -x(x-1)(x+1)$ and a table of $x$ values. We need to find the corresponding $y$ values for $x = -2, -1, -\frac{1}{2}, 0, \frac{1}{2}, 1, 2$.

1. Problem Description

We are given the equation $y = -x(x-1)(x+1)$ and a table of $x$ values. We need to find the corresponding $y$ values for $x = -2, -1, -\frac{1}{2}, 0, \frac{1}{2}, 1, 2$.

2. Solution Steps

We will substitute each $x$ value into the equation $y = -x(x-1)(x+1)$ to find the corresponding $y$ value.

* For $x = -2$:

$y = -(-2)(-2-1)(-2+1) = 2(-3)(-1) = 2(3) = 6$

* For $x = -1$:

$y = -(-1)(-1-1)(-1+1) = 1(-2)(0) = 0$

* For $x = -\frac{1}{2}$:

$y = -(-\frac{1}{2})(-\frac{1}{2}-1)(-\frac{1}{2}+1) = \frac{1}{2}(-\frac{3}{2})(\frac{1}{2}) = \frac{1}{2}(-\frac{3}{4}) = -\frac{3}{8}$

* For $x = 0$:

$y = -(0)(0-1)(0+1) = 0(-1)(1) = 0$

* For $x = \frac{1}{2}$:

$y = -(\frac{1}{2})(\frac{1}{2}-1)(\frac{1}{2}+1) = -\frac{1}{2}(-\frac{1}{2})(\frac{3}{2}) = -\frac{1}{2}(-\frac{3}{4}) = \frac{3}{8}$

* For $x = 1$:

$y = -(1)(1-1)(1+1) = -1(0)(2) = 0$

* For $x = 2$:

$y = -(2)(2-1)(2+1) = -2(1)(3) = -6$

3. Final Answer

The corresponding $y$ values are:

* $x = -2, y = 6$

* $x = -1, y = 0$

* $x = -\frac{1}{2}, y = -\frac{3}{8}$

* $x = 0, y = 0$

* $x = \frac{1}{2}, y = \frac{3}{8}$

* $x = 1, y = 0$

* $x = 2, y = -6$