The graph of y = ax² is a curve called a parabola.
Characteristics of a Parabola
- The vertex is the origin (0, 0)
- It is symmetrical about the y-axis
- a > 0: opens upward; a < 0: opens downward
- The larger |a| is, the narrower (steeper) the parabola
📘 Example ①
Compare the graphs of y = x² and y = 2x².
Answer:Both are parabolas with the origin as the vertex and symmetry about the y-axis. y = 2x² is narrower (steeper). When x = 1, y = 1 vs y = 2.
Compare the graphs of y = x² and y = 2x².
Answer:Both are parabolas with the origin as the vertex and symmetry about the y-axis. y = 2x² is narrower (steeper). When x = 1, y = 1 vs y = 2.
💡 Key Point
- The sign of a → direction in which the graph opens
- The size of |a| → width (narrowness) of the parabola
Practice Problems
- Describe the difference between the graphs of y = −x² and y = −3x².
Answers and Explanations
- Answer:Both are downward-opening parabolas. y = −3x² is narrower.