1. The problem states that the graph of the function $g(x) = mx^2$ is a parabola with vertex at the origin $(0,0)$ and passes through the point $(-2, 20)$. We need to find the value of $m$. 2. Since the vertex is at the origin, the function is of the form $g(x) = mx^2$. 3. Substitute the point $(-2, 20)$ into the equation to find $m$: $$20 = m(-2)^2$$ 4. Simplify the right side: $$20 = m \times 4$$ 5. Solve for $m$: $$m = \frac{20}{4} = 5$$ 6. Therefore, the value of $m$ is 5. Final answer: $m = 5$