https://file.aiquickdraw.com/mathbot/file/172572703449816l8jtf5.jpg

Here is the graph comparing the original function \( y = x^2 + 1 \) (in blue) with the transformed function \( y = -\left( \frac{x+2}{2} \right)^2 \) (in red, dashed line). As you can see:

- The transformed graph is reflected across the x-axis (upside down),
- It is horizontally stretched,
- It is shifted 2 units to the left, and
- The vertical translation of 1 up does not apply here due to the structure of the transformation.

Do you have any questions or would you like more details on these transformations?

Here are some related questions to further your understanding:

1. How would the graph change if the horizontal stretch factor was 3 instead of 2?
2. What would happen if we added a vertical stretch by a factor of 2 instead of the reflection?
3. How do translations affect the vertex of a parabola?
4. What if the equation was \( y = x^3 + 1 \)? How would the transformations apply?
5. Can you identify other transformations from the given graph?

**Tip:** Always apply horizontal transformations to the \( x \)-term before applying vertical transformations.

On the graph of y = x^2 + 1 below, perform the following transformations: horizontal stretch by 2, vertical reflection about x-axis, horizontal translation 2 units left, vertical translation 1 unit up.

Explore the transformations of the quadratic function y = x^2 + 1, including a horizontal stretch, vertical reflection, and translations. This guide breaks down each step with a detailed explanation and graphical comparison, perfect for high school students learning algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation