Okay, I have a graph of the f(x). It is a parabola that opens up. What does the graph of f(|x|) look like (the absolute value). Is it the same, or flipped or translated? Can someone describe what it looks like to me please :)

plug in numbers and see for yourself!

y=x^2
y=(|x|)^2

are they or they not identical?

The absolute value of x is always positive; so is the square. So the shape will remain invariant under this transformation, and so will be its position.

Sure! To understand what the graph of f(|x|) looks like, let's break it down step by step.

1. Absolute Value Function: The absolute value function, denoted as |x|, takes the input value (x) and returns its positive magnitude. This means that if x is positive, |x| remains the same, but if x is negative, |x| flips the sign to make it positive. For example, |3| = 3, |-2| = 2, and |0| = 0.

2. Applying Absolute Value to f(x): In this case, you're applying the absolute value function to the original function f(x) which is a parabola opening upward. When you replace x in f(x) with |x|, it means you're considering the positive magnitude of x only, regardless of its initial sign.

3. Flipping the Negative Part: Since f(x) is a parabola that opens upward, when you replace x with |x|, the negative values of x get flipped to positive values. Therefore, the negative part of the graph of f(x) will be reflected or "flipped" across the y-axis.

4. Overall Look: The graph of f(|x|) will still have the same shape as the original graph of f(x), but the negative part will be mirrored or flipped across the y-axis. The positive part of f(x) remains unchanged.

In summary, applying the absolute value to f(x) flips the negative part of the original parabolic graph across the y-axis, while the positive part remains the same.