The uploaded image contains three mathematical functions:

1. $f(x) = 2x^2$
2. $f(x) = (x - 2)^2$
3. $f(x) = (x + 2)^2$

Here’s a brief explanation of each:

1. $f(x) = 2x^2$:

   • This is a parabola that opens upwards, with its vertex at the origin $(0, 0)$.
   • The coefficient $2$ makes the parabola narrower than $x^2$.

2. $f(x) = (x - 2)^2$:

   • This is another parabola, but it is horizontally shifted 2 units to the right compared to $x^2$.
   • Its vertex is at $(2, 0)$.

3. $f(x) = (x + 2)^2$:

   • This parabola is shifted 2 units to the left compared to $x^2$.
   • Its vertex is at $(-2, 0)$.

Would you like a graph or further analysis of these functions?

Here are 5 related questions to deepen your understanding:

1. How does the coefficient of $x^2$ (e.g., $2$ in $2x^2$) affect the shape of a parabola?
2. What is the general equation for a parabola and how do you identify its vertex?
3. How does shifting affect the equation of a function?
4. Can these parabolas intersect? If so, how can we find their points of intersection?
5. How do transformations of functions apply to real-world situations?

Tip: To better understand the transformations of a function, plot the original and transformed functions on the same graph and observe the changes.