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How does the value of in each function affect its graph?.
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Q. How does the value of in each function affect its graph?.
- Consider Function : Let's consider the function and see what happens when we change the value of .
- Positive : U-shaped Parabola: If is positive, the graph opens upwards, like a regular U-shaped parabola.
- Negative : Downwards Parabola: If is negative, the graph opens downwards, like an upside-down U.
- Absolute Value of : Steeper Parabola: The larger the absolute value of , the steeper the parabola; it gets narrower.
- Absolute Value of : Wider Parabola: The smaller the absolute value of (but not ), the wider the parabola; it flattens out.
- Zero : Horizontal Line: If is zero, then , which is just , and the graph would be a horizontal line.
