To solve for $a$ in the equation $y = a(x - h)^2 + k$, follow these steps:

Step 1: Isolate the term with $a$.

Start by subtracting $k$ from both sides of the equation: $y - k = a(x - h)^2$

Step 2: Solve for $a$.

Now, divide both sides of the equation by $(x - h)^2$: $a = \frac{y - k}{(x - h)^2}$

Thus, the solution for $a$ is: $a = \frac{y - k}{(x - h)^2}$

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you solve for $h$ or $k$ in the same equation?
2. What does $a$ represent in the context of a parabolic function?
3. How would you find the vertex of the parabola given the equation $y = a(x - h)^2 + k$?
4. How does the value of $a$ affect the shape of the parabola?
5. Can you transform this equation into the standard form $y = ax^2 + bx + c$?

Tip: In this quadratic form, $a$ controls the "width" and direction of the parabola. A larger $|a|$ makes the parabola narrower, and a negative $a$ flips it upside down.