https://file.aiquickdraw.com/mathbot/file/1728608827730ft211xq2.jpg

The question asks to graph the function \( f(x) = x^2 - 2 \) and describe how it was translated from the function \( f(x) = x^2 \).

### Translation description:
The base function is \( f(x) = x^2 \), which is a standard parabola with its vertex at the origin (0, 0). The function \( f(x) = x^2 - 2 \) can be seen as a vertical translation of \( f(x) = x^2 \). The "-2" means the graph is shifted downward by 2 units. Therefore, the vertex of the parabola moves from (0, 0) to (0, -2).

In summary:
- **Vertical Translation**: The graph is shifted 2 units **downward**.

Would you like further details or help with graphing it? Here are five questions to expand on this topic:

1. How do horizontal translations affect the graph of a quadratic function?
2. What happens to the graph of \( f(x) = x^2 \) when a coefficient is added to \( x^2 \) (e.g., \( f(x) = 2x^2 \))?
3. How does the graph change if the function were \( f(x) = (x - 2)^2 \)?
4. Can you explain how to determine the vertex of a quadratic function?
5. What effect does a negative sign before the \( x^2 \) term have on the shape of the parabola?

**Tip:** When graphing quadratic functions, always start by identifying the vertex and direction of the parabola (whether it opens up or down).

Graph the function f(x) = x^2 - 2 and describe how it was translated from f(x) = x^2.

Learn how to graph the quadratic function f(x) = x^2 - 2 and understand its translation from the base function f(x) = x^2. This problem covers key algebra concepts, including vertical shifts in graphing quadratic functions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation