This image depicts two parabolas, labeled $f$ (blue curve) and $g$ (green curve). Both graphs represent quadratic functions. Let us analyze their properties based on the image:

1. General Observations:

   • $f(x)$: A parabola that opens upwards and has its vertex at approximately $(-1, 1)$.
   • $g(x)$: A parabola that opens upwards and has its vertex at approximately $(3, 1)$.

2. Intercepts:

   • The $y$-intercept for $f(x)$ is approximately 2.
   • The $y$-intercept for $g(x)$ is approximately 10.

3. Intersection:

   • The two parabolas intersect at around $x = 1$ and $x = 2$.

Would you like to explore:

1. The equations of the functions $f(x)$ and $g(x)$?
2. The intersection points in detail?
3. Any transformations between $f(x)$ and $g(x)$?
4. Specific properties such as axis of symmetry or vertex forms?
5. The domain and range of both functions?

Tip: Parabolas in the form $f(x) = ax^2 + bx + c$ can be analyzed for their vertex, direction, and width by adjusting the coefficients $a$, $b$, and $c$.