The graph of f, of, x, equals, 2, x, squared*f*(*x*)=2*x*2 is given below. Write the equation of a function g, of, x*g*(*x*) which would reflect the graph of f, of, x*f*(*x*) over the x-axis.

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To reflect the graph of \( f(x) = 2x^2 \) over the x-axis, we need to multiply the function by \(-1\). Reflecting a graph over the x-axis changes the sign of the output values of the function.

So, the equation of the reflected function \( g(x) \) would be:

\[
g(x) = -f(x) = -2x^2
\]

This means that every point on the graph of \( f(x) = 2x^2 \) will have its y-coordinate flipped to its negative counterpart.

Would you like further details on graph reflection or any other concept related to this?

Here are 5 related questions to deepen your understanding:
1. How do you reflect a graph over the y-axis?
2. What is the effect of reflecting a graph over the line \( y = x \)?
3. How does scaling the function vertically or horizontally change the graph?
4. What happens to the graph if you shift \( f(x) = 2x^2 \) vertically or horizontally?
5. How do the intercepts of the graph change after a reflection over the x-axis?

**Tip:** Reflecting a graph over the x-axis always changes the sign of the function values without altering the x-values.

The graph of f(x) = 2x^2 is given below. Write the equation of a function g(x) which would reflect the graph of f(x) over the x-axis.

Discover how to reflect the quadratic function f(x) = 2x^2 over the x-axis to find g(x). This problem explores key algebraic concepts of graph transformations and reflections, perfect for students in Grades 8-10.

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