Graph the equation $y=-x^{2}-8 x-12$ on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Click to plot points. Click points to delete them.

Step 1 ：First, we find the roots of the equation. The roots of the equation are the x-values for which y = 0. We can find these by setting the equation equal to zero and solving for x. This can be done using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where a, b, and c are the coefficients of the quadratic equation \(ax^2 + bx + c = 0\). In this case, a = -1, b = -8, and c = -12.

Step 2 ：The roots of the equation are -6 and -2.

Step 3 ：The vertex of a parabola given by the equation \(y = ax^2 + bx + c\) is the point (h, k), where \(h = \frac{-b}{2a}\) and \(k = c - \frac{b^2}{4a}\).

Step 4 ：The vertex of the parabola is at (-4, 4).

Step 5 ：Now we need to find two more points to plot. We can do this by choosing two x-values and calculating the corresponding y-values using the equation \(y = -x^2 - 8x - 12\).

Step 6 ：The additional points to plot are (-7, -5) and (-1, -5).

Step 7 ：Now we have five points: the roots (-6, 0) and (-2, 0), the vertex (-4, 4), and the additional points (-7, -5) and (-1, -5). These points can be used to graph the equation \(y = -x^2 - 8x - 12\).

Step 8 ：\(\boxed{\text{The five points to plot are (-6, 0), (-2, 0), (-4, 4), (-7, -5), and (-1, -5).}}\)