We study functions in the form y = ax²（a ≠ 0）. This is a relationship in which y is proportional to the square of x.
📘 Example ①
For y = 2x², find the values of y when x = 1, 2, and 3.
Answer:x=1: y=2、x=2: y=8、x=3: y=18
For y = 2x², find the values of y when x = 1, 2, and 3.
Answer:x=1: y=2、x=2: y=8、x=3: y=18
📘 Example ②
For y = ax², when x = 3 and y = 18, find a.
Answer:18 = a × 9 → a = 2
For y = ax², when x = 3 and y = 18, find a.
Answer:18 = a × 9 → a = 2
💡 Key Point
- y = ax²: when x doubles, y becomes four times as large
- It always passes through the origin (0, 0)
- When a > 0, it opens upward; when a < 0, it opens downward
Practice Problems
- For y = 3x², find y when x = −2.
- For y = ax², find a when x = 2 and y = −12.
Answers and Explanations
- Answer:y = 12。3×4=12。
- Answer:a = −3。−12 = 4a → a = −3。