If the graph of f(x)=x2�(�)=�2, how will the graph be affected if it is changed to f(x)=3x2�(�)=3�2?

A. 

The parabola will be translated up.

B. 

The parabola will be narrower

C. 

The parabola will be translated down.

D. 

The parabola will be wider.

When the function \( f(x) = x^2 \) is changed to \( f(x) = 3x^2 \), the coefficient of \( x^2 \) is increased from 1 to 3.

This affects the **vertical stretch** of the parabola. Specifically, the graph of \( f(x) = 3x^2 \) will be narrower compared to the graph of \( f(x) = x^2 \), because multiplying by a factor greater than 1 vertically compresses the graph.

So the correct answer is:

**B. The parabola will be narrower.**

Do you want details or have any questions?

Here are 8 questions related to this problem:

1. What happens to a parabola when the coefficient of \( x^2 \) is negative?
2. How does changing the coefficient of \( x^2 \) affect the vertex of the parabola?
3. What does the term "narrower" mean in the context of a parabola's graph?
4. How would the graph of \( f(x) = \frac{1}{2}x^2 \) compare to \( f(x) = x^2 \)?
5. What is the effect of adding a constant to the function \( f(x) = x^2 \)?
6. How does the graph change if the function is \( f(x) = x^2 + 4 \) instead?
7. What is the vertex form of a parabola, and how can it help in graph transformations?
8. How do horizontal shifts differ from vertical stretches in graph transformations?

**Tip:** When dealing with transformations of functions, always focus on how coefficients and constants affect the shape and position of the graph.

Understand how changing the coefficient affects the graph of a quadratic function. Learn about vertical stretch in quadratic functions with detailed explanations and examples. Suitable for students studying quadratic equations and graph transformations in Grades 9-12.

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