1. The original function is given as $f(x) = -x^2$. 2. We apply a vertical stretch to $f(x)$ by a factor of 8. A vertical stretch multiplies the $y$-values by the stretch factor. 3. Therefore, the transformed function is $$g(x) = 8 imes f(x) = 8 imes (-x^2) = -8x^2.$$ 4. This means the parabola opens downward (since the coefficient is negative) and is narrower than the original $f(x)$ because of the stretch. 5. The vertex of both $f(x)$ and $g(x)$ is at the origin $(0,0)$. 6. For graphing, use the formula $$g(x) = -8x^2$$ with the given coordinate range from -12 to 12 on both axes. This transformation changes the steepness but not the location of the vertex.