We organize the properties of y = ax².
Summary of the Properties of y = ax²
- A parabola with the origin as its vertex and symmetry about the y-axis
- a > 0 → opens upward (minimum value = 0)
- a < 0 → opens downward (maximum value = 0)
- The larger |a| is, the narrower the parabola
📘 Example ①
For y = −2x² and 1 ≤ x ≤ 3, find the range of y.
Answer:Since a < 0, y becomes smaller as x becomes larger. When x=1, y=−2 (maximum); when x=3, y=−18 (minimum).−18 ≤ y ≤ −2
For y = −2x² and 1 ≤ x ≤ 3, find the range of y.
Answer:Since a < 0, y becomes smaller as x becomes larger. When x=1, y=−2 (maximum); when x=3, y=−18 (minimum).−18 ≤ y ≤ −2
Practice Problems
- For y = −x² and −2 ≤ x ≤ 3, find the range of y.
Answers and Explanations
- Answer:−9 ≤ y ≤ 0。When x=0, y=0 (maximum); when x=3, y=−9 (minimum)。