PAIBOTLearn
Sign inSign up

Rate of change

The function y = ax²

Japanese school year: Junior high 3

What you learn

You will learn how to calculate the rate of change for y=ax² and understand why it varies across intervals, unlike linear functions. This concept is essential for determining average speeds in physics and serves as an introduction to calculus. Prior understanding of linear rates of change and function evaluation is recommended.

Go to practice

Key points

This is the basic definition for the rate of change. It is calculated as the ratio of the change in yy to the change in xx, and its value varies depending on the interval chosen.

y2−y1x2−x1(x1≠x2)\frac{y_2 - y_1}{x_2 - x_1} \quad (x_1 \neq x_2)

This formula calculates the rate of change for y=ax2y = ax^2 as xx increases from pp to qq. It is obtained quickly by multiplying the constant aa by the sum of the endpoints, (p+q)(p + q).

aq2−ap2q−p=a(p+q)(p≠q)\frac{aq^2 - ap^2}{q - p} = a(p + q) \quad (p \neq q)

Choose a set to practice.