Problem Analysis:
The task involves translating a given graph according to specific instructions. The original graph is provided, and we need to determine how it changes when translated as described in each question.
#### Key Concepts:
1.
Translation:
- Moving a graph horizontally or vertically without changing its shape.
- Horizontal translations affect the \( x \)-coordinate.
- Shifting right: Subtract from \( x \).
- Shifting left: Add to \( x \).
- Vertical translations affect the \( y \)-coordinate.
- Shifting up: Add to \( y \).
- Shifting down: Subtract from \( y \).
2.
Graph Characteristics:
- The original graph appears to be a parabola (a quadratic function).
- Translations will shift the entire graph but will not alter its shape.
---
Question 1: Translate the graph 2 units to the left.
#### Solution:
-
Translation Rule: Shifting 2 units to the left means adding 2 to the \( x \)-coordinate of every point on the graph.
-
Effect: Every point \((x, y)\) on the original graph will move to \((x + 2, y)\).
-
Visual Impact: The entire graph shifts 2 units to the left.
#### Correct Answer:
The correct graph after translating 2 units to the left is
option (c).
---
Question 2: Translate the graph 3 units down.
#### Solution:
-
Translation Rule: Shifting 3 units down means subtracting 3 from the \( y \)-coordinate of every point on the graph.
-
Effect: Every point \((x, y)\) on the original graph will move to \((x, y - 3)\).
-
Visual Impact: The entire graph shifts 3 units downward.
#### Correct Answer:
The correct graph after translating 3 units down is
option (d).
---
Final Answers:
1. For "Translate the graph 2 units to the left," the correct answer is:
(c).
2. For "Translate the graph 3 units down," the correct answer is:
(d).
Boxed Answers:
\[
\boxed{(c), (d)}
\]
Parent Tip: Review the logic above to help your child master the concept of algebra 2 parent functions and transformations worksheet.
