Fix the mistake: The Function y=ax² ②
Rate of Change ① Rate of Change of y=ax²
For y = ax², the rate of change is not constant (unlike a linear function).
Rate of change = increase in y ÷ increase in x
📘 Example ①
For y = 2x², find the rate of change when x increases from 1 to 3.
Answer:x=1 → y=2, x=3 → y=18. Rate of change = (18−2)/(3−1) = 16/2 = 8
For y = 2x², find the rate of change when x increases from 1 to 3.
Answer:x=1 → y=2, x=3 → y=18. Rate of change = (18−2)/(3−1) = 16/2 = 8
💡 Key Point
- Rate of change of y=ax² = a(x₁+x₂) (formula)
- Unlike a linear function, it changes depending on the value of x
Practice Problems
- For y = 3x², find the rate of change when x increases from 2 to 5.
Answer and Explanation
- Answer:21. x=2 → y=12, x=5 → y=75. (75−12)/(5−2)=63/3=21.
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