The image shows a set of parabolas labeled $y_1, y_2, y_3, y_4$, and the question asks which function best represents the parabola $y_2$.

From the options provided:

• $y = 2x^2$
• $y = (x - 2)^2$
• $y = x^2$
• $y = x^2 - 2$

The parabola $y_2$ is shifted downward compared to the standard parabola $y = x^2$, and it opens upward like a normal parabola. This means it should match a function of the form $y = x^2 - k$, where $k$ is a positive number indicating a downward shift.

Among the options, $y = x^2 - 2$ (the last option) matches this description as it represents a downward shift of 2 units. Therefore, the function that best represents $y_2$ is:

$y = x^2 - 2$

Would you like further clarification on this? Here are some related questions you might explore:

1. How do you determine the vertex of a parabola from its equation?
2. What changes occur when you adjust the coefficient of $x^2$ in a quadratic function?
3. How do horizontal shifts in quadratic equations affect the graph?
4. What is the significance of the constant term in a quadratic equation?
5. How can you find the equation of a parabola given its vertex and one point?

Tip: Remember, the constant term in a quadratic equation $y = ax^2 + bx + c$ tells you the vertical position of the vertex relative to the origin.