AlgebraStructure & Method · Book 1All Chapters

Variation

12-7Direct and Inverse Variation Involving Squares

Overview

Direct with square: y = kx². Inverse with square: y = k/x².

Key ideas

  • Find k using one pair (x, y).
  • y changes by a factor of (ratio)² when x changes.
  • Use the model to predict.

Worked examples

Example 1

Problem. y varies directly as x². y = 12 when x = 2. Find y when x = 5.

Solution. k = 3. y = 3(25) = 75.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    y = kx², y = 8 at x = 2. Find y at x = 3.

  2. 2.

    y = k/x², y = 4 at x = 3. Find k.

  3. 3.

    y = k/x², y = 9 at x = 1. Find y at x = 3.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    y varies directly with x². If y = 36 when x = 3, find y when x = 5.

  2. 2.

    The intensity of light varies inversely with the square of the distance. If intensity is 40 at 3 meters, what is it at 5 meters?