1. When the equation $y = -\frac{1}{2}(x + 4)^2 - 3$ is written in standard form $y = ax^2 + bx + c$, the value of $c$ is ___.
2. What is the vertex of the parabola given by the equation $y = -(x - 3)^2 + 4$?
3. What is the vertex of the parabola given by the equation $y = 3 + \frac{1}{2}(x + 4)^2$?
4. Write the equation $y = 2(x - 3)^2 + 4$ in standard form $y = ax^2 + bx + c$.
5. What are the coordinates of the vertex for the parabola with the equation $y = 5(x+1)^2 - 3$?
6. The quadratic equation $y = x^2 - 8x + 10$ has a vertex at $(x_v, y_v)$. What is the value of $x_v$? ___
7. When the equation $y = x^2 + 10x + 29$ is written in vertex form $y = (x - x_v)^2 + y_v$, what is the value of $y_v$? ___
8. Which equation is written in the correct vertex form for a parabola with a vertex at $(-6, 2)$?
9. A parabola passes through the points $(0, 5)$, $(1, 8)$, and $(2, 15)$. If its equation is $y = ax^2 + bx + c$, what is the value of $b$? ___