The graph of y = ax²（a ≠ 0）is a parabola. Its vertex is the origin, and its axis is the y-axis.
Basics of Parabolas
- a > 0 → opens upward
- a < 0 → opens downward
- The larger |a| is, the narrower the parabola
Example ①
Compare the characteristics of the graphs of y = 2x² and y = -x².
Answer: y = 2x²: opens upward and is narrow. y = -x²: opens downward and is wider than y = x². Both have the origin as their vertex.
Compare the characteristics of the graphs of y = 2x² and y = -x².
Answer: y = 2x²: opens upward and is narrow. y = -x²: opens downward and is wider than y = x². Both have the origin as their vertex.
Key Point
- A parabola with the origin as its vertex and the y-axis as its axis
- The sign of a → opening direction, |a| → width
Practice Problems
- When comparing y = 3x² and y = (1/2)x², state which is the narrower parabola.
Answers and Explanations
- Answer: y = 3x²（because |3| > |1/2|, it is narrower）.