Function 
g can be thought of as a scaled version of 
f(x)=x^2  Write the equation for 
g(x)

The function \( g(x) \) is a scaled version of \( f(x) = x^2 \). Scaling a function means multiplying it by a constant factor, which changes the amplitude of the graph but preserves its general shape.

So, the equation for \( g(x) \) can be written as:

\[
g(x) = a \cdot f(x) = a \cdot x^2
\]

where \( a \) is the scaling factor. If \( a > 1 \), the graph of \( g(x) \) is stretched vertically. If \( 0 < a < 1 \), the graph is compressed vertically. If \( a < 0 \), the graph is reflected and scaled.

Would you like to specify a value for \( a \) or get more details on how scaling affects the graph?

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Here are five related questions:
1. What happens to the graph of \( f(x) = x^2 \) if \( a = -2 \) in \( g(x) = a \cdot x^2 \)?
2. How does scaling a function horizontally differ from vertical scaling?
3. Can you give an example of a real-life situation where scaling a quadratic function would be useful?
4. What is the effect of adding a constant to the equation \( g(x) = a \cdot x^2 + b \)?
5. How would the function change if we also translate \( f(x) = x^2 \) vertically?

**Tip:** Scaling functions vertically by a factor \( a \) only affects the "steepness" or "width" of the graph, not its basic parabolic shape.

Function g can be thought of as a scaled version of f(x)=x^2. Write the equation for g(x).

Explore how scaling affects quadratic functions by learning how to write the equation for g(x), a scaled version of f(x)=x^2. This guide explains key concepts, including vertical stretching, compression, and reflections. Suitable for students in Grades 9-12.

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