Use this worksheet to practice writing quadratic equations by analyzing the vertex and shape of 16 different parabolas.

It looks like you've uploaded an image containing 16 graphs of quadratic functions (parabolas), and the task is to write the equation of each graph.

Since I can't view images directly, I need you to describe or provide details about the graphs — such as:

- The vertex of each parabola (coordinates),
- Whether it opens upward or downward,
- Any x-intercepts or y-intercepts,
- Whether it's stretched or compressed,
- Or any other key features.

Alternatively, if you can describe one or two of the graphs in detail (e.g., “Graph 1 has a vertex at (2, -1), opens upward, and passes through (0, 3)”), I can help you find the equation.

But since this is a common type of problem, let me give you a general method for finding the equation of a parabola from its graph.

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🔧 General Method: Finding the Equation of a Parabola

Quadratic equations can be written in vertex form:

$$
y = a(x - h)^2 + k
$$

Where:
- $(h, k)$ is the vertex of the parabola,
- $a$ determines the direction and width:
- If $a > 0$: opens upward,
- If $a < 0$: opens downward,
- $|a|$ controls how wide/narrow it is.

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📌 Steps to Solve:

1. Find the vertex $(h, k)$.
2. Determine the direction (up/down) → sign of $a$.
3. Use another point on the graph (like y-intercept or x-intercept) to solve for $a$.
4. Plug values into the vertex form.

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✔ Example (Hypothetical):

Suppose Graph 1 has:
- Vertex at $(1, -2)$,
- Opens upward,
- Passes through $(0, -1)$.

Then:
$$
y = a(x - 1)^2 - 2
$$
Plug in $(0, -1)$:
$$
-1 = a(0 - 1)^2 - 2 \Rightarrow -1 = a(1) - 2 \Rightarrow a = 1
$$
So the equation is:
$$
y = (x - 1)^2 - 2
$$

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🔍 For Your Image:

Since there are 16 graphs, here’s what I recommend:

Please describe one or more graphs with:
- Vertex coordinates,
- Direction (up/down),
- One other point it passes through (like intercepts).

Or, if possible, upload the image again via a text-based description (e.g., grid coordinates), and I’ll walk you through solving all 16.

Alternatively, if these are standard textbook problems, they might follow patterns like:

- Vertex at origin: $y = ax^2$
- Shifted right/left/up/down: $y = a(x - h)^2 + k$
- Intercepts given: use factored form $y = a(x - r)(x - s)$

Let me know how you'd like to proceed!