When the range of x is given, we find the range of y.
📘 Example ①
For y = 2x² and −2 ≤ x ≤ 3, find the range of y.
Answer:When x=0, y=0 (minimum). When x=3, y=18 (maximum). When x=−2, y=8。
→ 0 ≤ y ≤ 18
For y = 2x² and −2 ≤ x ≤ 3, find the range of y.
Answer:When x=0, y=0 (minimum). When x=3, y=18 (maximum). When x=−2, y=8。
→ 0 ≤ y ≤ 18
💡 Key Point
- a > 0: The minimum value is 0 at the vertex x=0. The larger the absolute value of x, the larger y becomes.
- Check whether x=0 is included in the range
Practice Problems
- For y = x² and −3 ≤ x ≤ 1, find the range of y.
Answers and Explanations
- Answer:0 ≤ y ≤ 9。The minimum is 0 when x=0, and the maximum is 9 when x=−3。