We find a in y = ax² from a graph or given conditions.
📘 Example ①
For y = ax², find a when the graph passes through the point (−3, 18).
Answer:18 = a × 9 → a = 2。Therefore, y = 2x²。
For y = ax², find a when the graph passes through the point (−3, 18).
Answer:18 = a × 9 → a = 2。Therefore, y = 2x²。
💡 Key Point
- Substitute the coordinates (x, y) of a point on the graph into y = ax² to find a
- x² is always positive → the sign of y determines the sign of a
Practice Problems
- For y = ax², find a when the graph passes through the point (4, −8).
Answers and Explanations
- Answer:a = −1/2。−8 = 16a → a = −1/2。