1. The problem is to find the value of $a$ in the quadratic function given in vertex form: $$y = a(x - h)^2 + k$$ where the vertex is $(h, k)$ and the parabola passes through a given point. 2. For the first quadratic function, the vertex is at $(0,0)$ and it passes through the point $(0,0)$. 3. Substitute the vertex and the point into the equation: $$y = a(x - 0)^2 + 0 = a x^2$$ At the point $(0,0)$: $$0 = a \times 0^2 = 0$$ This is true for any $a$, so $a$ is not determined from this point alone. 4. For the second quadratic function, the vertex is at $(0,-2)$ and it passes through the point $(0,-2)$. 5. Substitute the vertex and the point into the equation: $$y = a(x - 0)^2 - 2 = a x^2 - 2$$ At the point $(0,-2)$: $$-2 = a \times 0^2 - 2 = -2$$ Again, this is true for any $a$, so $a$ is not determined from this point alone. 6. Since the pass point is the same as the vertex in both cases, the value of $a$ cannot be determined uniquely from the given information. Final answer: $a$ is indeterminate with the given points because the pass point coincides with the vertex.