Review the rate of change, intersections, and applications of y = ax².
📘 Example ①
For y = 2x², find the rate of change when x increases from −1 to 2.
Answer:x=−1 → y=2, x=2 → y=8. (8−2)/(2−(−1)) = 6/3 = 2
For y = 2x², find the rate of change when x increases from −1 to 2.
Answer:x=−1 → y=2, x=2 → y=8. (8−2)/(2−(−1)) = 6/3 = 2
💡 Key Point
- Rate of change = Δy / Δx = a(x₁ + x₂)
- Intersections: Set the y-values equal and solve
Practice Problems
- Find the intersections of y = x² and y = −x + 6.
Answer and Explanation
- Answer:(2, 4) and (−3, 9). x²=−x+6 → x²+x−6=0 → (x+3)(x−2)=0.