The given equation is:

\[
y = 2(x - 5)^2
\]

This is the equation of a parabola in vertex form, where:

\[
y = a(x - h)^2 + k
\]

In this case:
- \( a = 2 \)
- \( h = 5 \)
- \( k = 0 \)

### Key Characteristics:
1. **Vertex**: The vertex of the parabola is at \( (h, k) = (5, 0) \).
2. **Direction**: Since \( a = 2 \) is positive, the parabola opens **upward**.
3. **Stretch**: The value \( a = 2 \) makes the parabola narrower than the standard \( y = (x - h)^2 \), as the factor of 2 vertically stretches it.
4. **Axis of Symmetry**: The parabola is symmetric about the vertical line \( x = 5 \).

Would you like further details or have any specific questions about this equation?

Here are 5 related questions:
1. What are the key features of a parabola in vertex form?
2. How does changing the value of \( a \) affect the shape of the parabola?
3. What is the effect of shifting the vertex horizontally or vertically?
4. Can we convert the vertex form to the standard quadratic form \( y = ax^2 + bx + c \)?
5. How do we find the focus and directrix of this parabola?

**Tip**: The vertex form is great for quickly identifying the vertex and direction of a parabola!

Explore the quadratic function y = 2(x - 5)^2 and learn how to identify the vertex, axis of symmetry, and the direction of the parabola. This detailed explanation covers key concepts in Algebra for students in Grades 9-10.

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