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The image describes a mathematical problem involving a parabola. Here's the text extracted from the image:

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**Board Work**

A vertex at (1, 3) and a point along the graph (7, 6).

1. Write the given parts.  
2. Sketch the possible graphs.  
3. Solve for the values of **h**, **k**, and **p**.  
4. Find the equation.

---

This appears to be a problem related to parabolas, where the vertex form of a parabola is usually given as:

\[
y = a(x - h)^2 + k
\]

where \((h, k)\) is the vertex, and the point \((7, 6)\) lies on the parabola.

We are tasked with determining the equation of the parabola.

### Let's solve this step-by-step:

1. **Given parts:**
   - Vertex: \((h, k) = (1, 3)\)
   - A point on the parabola: \((x, y) = (7, 6)\)

2. **Write the vertex form:**
   \[
   y = a(x - h)^2 + k
   \]
   Substituting \((h, k)\) as \((1, 3)\):
   \[
   y = a(x - 1)^2 + 3
   \]

3. **Use the point \((7, 6)\) to solve for \(a\):**

   Substituting \(x = 7\) and \(y = 6\):
   \[
   6 = a(7 - 1)^2 + 3
   \]
   Simplifying:
   \[
   6 = a(6)^2 + 3
   \]
   \[
   6 = 36a + 3
   \]
   \[
   36a = 3
   \]
   \[
   a = \frac{1}{12}
   \]

4. **Final equation:**

   Now substitute \(a = \frac{1}{12}\) into the equation:
   \[
   y = \frac{1}{12}(x - 1)^2 + 3
   \]

This is the equation of the parabola.

---

Would you like any further details or clarifications?

### Here are 5 questions to expand on this:
1. How do you convert a parabola from vertex form to standard form?
2. What happens to the graph of the parabola when the value of \(a\) changes?
3. How do you find the focus and directrix of a parabola from its vertex form?
4. What is the general form of a parabola with a horizontal axis?
5. Can this parabola be reflected, and how would that affect its equation?

### Tip:
When solving parabolas, always use known points on the graph to determine the coefficient \(a\), which helps describe the "width" and direction of the parabola.

A vertex at (1, 3) and a point along the graph (7, 6). Write the given parts. Sketch the possible graphs. Solve for the values of h, k, and p. Find the equation.

Learn how to find the equation of a parabola given a vertex at (1, 3) and a point along the graph (7, 6). This step-by-step solution uses the vertex form of a quadratic equation and algebraic methods to determine the value of 'a' and the final equation.

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