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.

Learn how to solve for 'a' in the vertex form equation of a parabola y = a(x - h)^2 + k. This step-by-step solution covers algebraic concepts including quadratic functions and transformations, suitable for students in Grades 9-11.

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