Math Problem Statement

Move the slider so that the graph of y = x^2 gets shifted to the right 2 units. Then type the new function f(x) in the answer box.

Solution

The graph provided shows the function f(x)=x2f(x) = x^2, which is a basic parabola centered at the origin. You are asked to shift this graph 2 units to the right.

When shifting a function horizontally, the general transformation is:

f(xh)f(x - h)

Where hh is the horizontal shift. In this case, the shift is 2 units to the right, so the new function becomes:

f(x)=(x2)2f(x) = (x - 2)^2

Thus, after shifting the graph 2 units to the right, the transformed function is:

f(x)=(x2)2f(x) = (x - 2)^2

Would you like more details or explanations?

Here are five related questions you might find helpful:

  1. How would the function change if the shift was 3 units to the left instead?
  2. What happens if you apply a vertical shift instead of a horizontal one?
  3. How does the vertex of the parabola change with horizontal shifts?
  4. Can you describe how stretching or compressing affects the graph?
  5. What if we shift the graph vertically and horizontally simultaneously?

Tip: Remember, shifting right is done by subtracting a positive value from xx, while shifting left is done by adding a value.

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Math Problem Analysis

Mathematical Concepts

Functions
Quadratic Functions
Transformations

Formulas

f(x - h): Horizontal shift transformation for functions
Standard quadratic form: f(x) = x^2

Theorems

Transformation of functions

Suitable Grade Level

Grades 8-10