Quadratic Function Worksheet: Write the quadratic function for each graph.

Since I can't view or access images directly, I can’t see the specific graphs in your uploaded image. However, I can guide you through how to write a quadratic function for each graph based on typical problems like this.

---

🔷 General Approach to Finding the Quadratic Function from a Graph

A quadratic function is generally written in one of these forms:

1. Standard Form:
$$
y = ax^2 + bx + c
$$

2. Vertex Form:
$$
y = a(x - h)^2 + k
$$
where $(h, k)$ is the vertex of the parabola.

3. Intercept Form (if x-intercepts are known):
$$
y = a(x - r_1)(x - r_2)
$$
where $r_1$ and $r_2$ are the x-intercepts.

---

✔ Step-by-Step Strategy

For each graph, follow these steps:

#### 1. Identify the vertex $(h, k)$
- The vertex is the highest or lowest point of the parabola.
- Use the grid to find its coordinates.

#### 2. Determine the direction of opening
- If the parabola opens up, $a > 0$
- If it opens down, $a < 0$

#### 3. Find another point on the graph (not the vertex), e.g., the y-intercept or an x-intercept.

#### 4. Use vertex form and solve for $a$
- Plug the vertex into $y = a(x - h)^2 + k$
- Plug in the other point to solve for $a$

#### 5. Write the equation

---

Let’s assume we have typical graphs like those found on such worksheets. Here's how you’d solve one example:

---

📌 Example Problem (Typical Graph)

Suppose Graph #1 has:
- Vertex at $(-1, 4)$
- Passes through point $(0, 3)$
- Opens downward

#### Step 1: Use vertex form
$$
y = a(x + 1)^2 + 4
$$

#### Step 2: Plug in $(0, 3)$
$$
3 = a(0 + 1)^2 + 4 \\
3 = a(1) + 4 \\
a = -1
$$

#### Final Equation:
$$
y = -(x + 1)^2 + 4
$$

You can expand it to standard form if needed:
$$
y = -(x^2 + 2x + 1) + 4 = -x^2 - 2x - 1 + 4 = -x^2 - 2x + 3
$$

---

🧩 For Each Graph in Your Worksheet

I’ll now give general guidance for each problem based on common patterns. Since I can't see the image, please describe each graph or tell me the key features (like vertex, intercepts, direction), and I’ll help write the function.

But here’s a template for what to look for:

| Graph | Vertex | Direction | X-intercepts | Y-intercept | Suggested Form |
|-------|--------|-----------|--------------|-------------|----------------|
| 1 | (-1, 4) | Down | (-3,0), (1,0) | (0,3) | Vertex or Intercept |
| 2 | (0, 2) | Up | (-2,0), (2,0) | (0,2) | Intercept or Vertex |
| 3 | (1, -4) | Up | (0,0), (2,0) | (0,0) | Intercept form |

---

💡 Tips:

- If the graph shows x-intercepts, use intercept form.
- If only vertex and one point are clear, use vertex form.
- If you know three points, use standard form and solve a system.

---

🔁 How to Proceed

Please describe each graph using:
- Coordinates of the vertex
- Whether it opens up or down
- Any visible x-intercepts or y-intercepts

Then I’ll write the quadratic function for each.

Alternatively, if you can transcribe the coordinates of key points from each graph, I can solve them all step by step.

Just let me know!