Understanding Shift in Curve Between y=x² and y=(x-2)²

Last Updated on Jul 31, 2023
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If you're intrigued by the fascinating world of graphs and functions, you've likely come across the concept of shifting graphs. This concept is not only crucial for understanding functions but also plays a significant role in the study of coordinate geometry. In this article, we'll delve into the details and solve a specific question: How much and in which direction does the curve shift between y=x² and y=(x-2)²?

To kick things off, it's important to understand that for any positive constant c, the graph of function y=f(x+c) shifts c units in the negative x direction. The magnitude of this shift is represented by the constant c.

Now, let's apply this principle to our question. Here, the value of c is -2. So, by the rules we've just discussed, the graph will shift 2 units in the positive x direction. In simpler terms, the y values that were initially at x will now occur at (x+2).

To better understand this, let's take a look at an example. In the original function, y=0 occurs at x=0, which is the origin. Now, let's see what happens with the new function y=(x-2)².

If we set y=0, we get 0=(x-2)². Taking the square root of both sides, we get x-2 = 0, which simplifies to x=2.

This means that y=0 now occurs at x=2. In other words, the graph has shifted 2 units in the positive x direction. This same principle applies to all values of y, leading to a shift of the entire graph.

It's fascinating, isn't it? How a simple change in the function can lead to a shift in the graph! We hope this explanation has helped clarify this concept for you. Remember, understanding the basics is the key to mastering any concept.

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Frequently Asked Questions

The shift in curve is calculated using the concept of shifting graphs. For a positive constant c, the graph of function y=f(x+c) shifts c units in the negative x direction. In this case, the value of c= -2, so the graph shifts 2 units in the positive x direction.

When the graph shifts in the positive x direction, it means that the values of y that occurred initially at x, will now occur at (x+2).

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