To find the equation of a parabola with its vertex at the origin and a focus at the point \((-8, 0)\), we can use the standard form of the parabola's equation. Since the focus is to the left of the vertex, the parabola opens to the left.
The standard form of a horizontally oriented parabola (opening left or right) with vertex at the origin is:
\[ y^2 = 4px \]
Here, \(p\) is the distance from the vertex to the focus. In this case, the focus is at \((-8, 0)\), which means \(p = -8\) (since it's to the left, we use a negative value).
Substituting \(p\) into the equation gives:
\[ y^2 = 4(-8)x \] \[ y^2 = -32x \]
Thus, the equation of the parabola is:
\[ y^2 = -32x \]
Therefore, the correct response is:
y squared equals negative 32 x.