The equation you provided is \( Y = a \times x^2 \). This is a quadratic equation, where:

- \( Y \) is the dependent variable.
- \( x \) is the independent variable.
- \( a \) is a constant coefficient that determines the shape and orientation of the parabola.

In this form, the equation represents a parabola that opens upwards if \( a > 0 \) or downwards if \( a < 0 \). The vertex of the parabola is at the origin \((0, 0)\), and the axis of symmetry is along the \(y\)-axis.

Would you like more details on how this equation behaves, or do you have any specific questions?

Here are 5 related questions to consider:

1. How does changing the value of \(a\) affect the width of the parabola?
2. What happens to the graph of the equation if \(a\) is negative?
3. Can you derive the vertex form of a quadratic equation from the standard form?
4. What are the roots of the quadratic equation \(Y = a \times x^2\) if \(Y = 0\)?
5. How can the equation \(Y = a \times x^2\) be applied in real-world scenarios?

**Tip:** When dealing with quadratic equations, always consider the sign and magnitude of the coefficient \(a\), as it significantly influences the graph's shape and direction.

Explore the quadratic equation Y = a * x^2 and its properties. This equation defines a parabola with the vertex at the origin and the axis of symmetry along the y-axis. Discover how the coefficient 'a' affects the shape and direction of the parabola. Suitable for Grades 7-9.

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