The graph you've uploaded shows multiple parabolic functions, each with different transformations. Let’s analyze the features of the graph to write an equation.

1. First Parabola (on the left):

   • This parabola opens upwards and appears to be vertically shifted upwards by about 6 units.
   • The vertex is located at $(-3, 6)$.

   The general equation for a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For this graph: $y = a(x + 3)^2 + 6$

2. Second Parabola (in the middle):

   • This parabola opens upwards and seems to be shifted horizontally to the right by about 2 units and vertically shifted down by 2 units.
   • The vertex is at $(1, -2)$.

   Using the same formula, the equation is: $y = a(x - 1)^2 - 2$

3. Third Parabola (on the right):

   • This parabola also opens upwards and is horizontally shifted right by 4 units, vertically shifted down by 4 units.
   • The vertex is at $(4, -4)$.

   Therefore, the equation for this graph is: $y = a(x - 4)^2 - 4$

Each of these equations is of the form $y = a(x - h)^2 + k$, where the constants $a$, $h$, and $k$ adjust the position and shape of the parabola.

Would you like to know more details about how these transformations work, or have any specific questions? Here are 5 related questions you could explore:

1. How do the coefficients $a$, $h$, and $k$ affect the graph of a parabola?
2. What happens when the value of $a$ is negative in a parabolic equation?
3. How do you find the vertex of a parabola from its equation?
4. How does horizontal shifting work in the equation of a parabola?
5. Can you describe the process for determining the transformation of a quadratic function from its graph?

Tip: The value of $a$ determines how "wide" or "narrow" the parabola is. A larger absolute value of $a$ makes the parabola narrower, while a smaller absolute value makes it wider.