Question
1. 29. To achieve a wider parabola from the graph of \( y=x^{2} \) using GeoGebra, you would: a. Subtract a number from \( x^{2} \) b. Multiply the entire equation by a coefficient less than 1 o. Add a number to \( x^{2} \) d. Multiply a by a coefficient less than 1
Ask by Weaver Graham. in the United States
Feb 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To make the parabola wider, multiply the equation by a coefficient less than 1.
Solution
To make the "bowl" of the parabola wider (i.e., less steep) than y = x², you need a vertical stretch factor that is less than 1. This means rewriting the function as y = a·x² with 0 < a < 1. Multiplying x² by a coefficient less than 1 decreases the overall y-values for each x, making the parabola wider.
So the correct answer is:
b. Multiply the entire equation by a coefficient less than 1
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Simplify this solution Extra Insights
To achieve a wider parabola from the graph of \( y=x^{2} \), you would multiply the equation by a coefficient less than 1 (option b). This decreases the "steepness" of the parabola, making it wider. For instance, changing the equation to \( y=0.5x^{2} \) stretches it horizontally. In mathematics, the shape of a parabola is heavily influenced by the coefficient of the \( x^{2} \) term. A larger coefficient results in a narrower parabola, while a smaller coefficient produces a wider shape. This property makes it easier to manipulate parabolic graphs for various applications, such as designing projectile paths or optimizing certain functions.
