The function you've provided is \( f(x) = 56x^2 \). This is a quadratic function, where the coefficient of \( x^2 \) is 56.

### Key Characteristics of the Function:

1. **Shape**: Since the coefficient of \( x^2 \) is positive, the parabola opens upwards.
2. **Vertex**: The vertex of this parabola is at the origin \((0,0)\), since there are no \( x \) or constant terms added.
3. **Axis of Symmetry**: The axis of symmetry is the vertical line \( x = 0 \).
4. **Y-intercept**: The y-intercept occurs at \( x = 0 \), and \( f(0) = 56 \times 0^2 = 0 \).
5. **Growth**: As \( |x| \) increases, \( f(x) \) grows rapidly due to the \( x^2 \) term.

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### Related Questions:
1. How do you find the vertex of a quadratic function?
2. What is the general form of a quadratic function?
3. How do you determine the axis of symmetry in a quadratic function?
4. What is the effect of changing the coefficient of \( x^2 \) on the graph of a parabola?
5. How do you calculate the roots (x-intercepts) of a quadratic equation?

**Tip:** The coefficient of \( x^2 \) determines the "width" of the parabola; a larger coefficient makes the parabola narrower, while a smaller coefficient makes it wider.

Explore the quadratic function f(x) = 56x^2 with a detailed explanation of its properties, including the vertex, axis of symmetry, and the behavior of its graph. This concept is crucial for students in Grades 9-10 learning about parabolas and quadratic equations.

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