if f(x)=x square then what is the graph of minus f(x)

If \( f(x) = x^2 \), then \( f(x) \) is a parabola opening upwards with its vertex at the origin (0,0).

To find the graph of \( -f(x) \):

1. Replace \( f(x) \) with \( x^2 \) to get \( -f(x) = -x^2 \).

The graph of \( -x^2 \) is a parabola opening downwards with its vertex also at the origin (0,0). This transformation reflects the original parabola \( f(x) = x^2 \) over the x-axis.

Would you like a graphical representation or further details on this topic?

Here are 5 questions you might want to ask:
1. How do I find the vertex of a parabola?
2. What are the transformations of the function \( f(x) = x^2 \)?
3. How do I graph \( f(x) = x^2 \) and \( -f(x) \) on the same coordinate plane?
4. What is the effect of negative coefficients on the graph of a quadratic function?
5. How do I find the axis of symmetry for a parabola?

**Tip:** Reflecting a function \( f(x) \) over the x-axis can be done by graphing \( -f(x) \).

Explore how to graph -f(x) when given f(x) = x^2. Learn about the transformation of a parabola and its reflection over the x-axis. Suitable for high school students studying quadratic functions and graph transformations.

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