What happens to the graph of the quadratic function y=a×square as the value of a becomes larger?

As the value of \( a \) in the quadratic function \( y = a \times x^2 \) becomes larger, the graph undergoes a few key changes:

1. **Vertical Stretch**: As \( a \) increases, the graph becomes narrower or "stretches" vertically. This is because the rate at which \( y \) increases for a given \( x \) becomes faster, so the parabola appears steeper.
  
2. **Direction**: The direction of the parabola remains the same (opening upward) as long as \( a > 0 \). If \( a \) is negative, the parabola flips and opens downward, but this doesn't change with an increase in the magnitude of \( a \).

In summary: When \( a \) becomes larger, the parabola gets steeper (narrower), but it still opens upwards if \( a \) is positive, or downwards if \( a \) is negative.

Would you like more details or have any questions?

Here are 5 related questions:
1. What happens to the graph when \( a \) becomes smaller?
2. How does the value of \( a \) affect the vertex of the parabola?
3. What is the role of \( a \) in determining the shape of other quadratic functions?
4. How do you find the vertex of a parabola given any quadratic equation?
5. How does changing \( a \) affect the symmetry of the graph?

**Tip**: The value of \( a \) primarily controls the "width" and "direction" of the parabola but doesn't affect the position of the vertex directly.

Explore how the value of 'a' impacts the graph of the quadratic function y = a × x^2. As 'a' increases, the graph undergoes a vertical stretch, making the parabola narrower. This tutorial covers key concepts in graph transformations, suitable for Grades 8-10.

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