The equation \( y = \frac{1}{4}x^2 \) represents a quadratic function. It is a parabola that opens upwards because the coefficient of \( x^2 \) is positive. Let's break this down:

- The general form of a quadratic equation is \( y = ax^2 + bx + c \). In your case, \( a = \frac{1}{4} \), and \( b = 0 \), \( c = 0 \).
- The vertex of the parabola is at the origin (0, 0).
- The coefficient \( \frac{1}{4} \) indicates that the parabola is wider than the standard \( y = x^2 \), since a smaller \( a \)-value causes the graph to stretch horizontally.

Would you like a more detailed analysis, or any specific information?

Here are 5 related questions to explore further:

1. How would the graph change if the coefficient were \( \frac{1}{2} \) instead of \( \frac{1}{4} \)?
2. What happens to the parabola if we add a constant term, say \( y = \frac{1}{4}x^2 + 3 \)?
3. How do you find the vertex form of a quadratic function, and how does it apply here?
4. Can you determine the axis of symmetry of the parabola? How would this change for a different quadratic?
5. What is the process for finding the roots of this quadratic function?

**Tip:** In quadratic functions, the coefficient of \( x^2 \) controls the "width" or "steepness" of the parabola. A smaller fraction makes the parabola wider, while a larger value makes it narrower.

Explore the quadratic function y = ¼x² with a step-by-step breakdown. Learn how the coefficient affects the width of the parabola and its vertex, along with key concepts like the axis of symmetry and graph transformations. Ideal for students in Grades 8-10.

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