Pre-Calculus 11 Notes

By: Gen L.

In partnership with Hyperion University, 2023

Lesson 2: Applications, Part 2

Example 1: Dimensions

  • The area of a rectangular table is . The length is more than the width. What are the dimensions of the table?
  1. Define Variables:
    • , , .
  2. Write the formula for the situation
  3. Fill in the formula
    • What do we know?

Solving Example 1, Part 1

  • Work with new equation to determine factors:
  • We have many tools we can use, which one?
    • Graph
    • Square-Root Principle
    • Factoring
    • Quadratic Formula
  • How about factoring?

Solving Example 1, Part 2

  • Remember: our equation is:
    • Let's try factoring the equation:
  • Now, let's solve for .
  • as an area is not possible. Since we cannot have a negative length, we call this an extraneous root.
  • .

Example 2: Object Heights

  • The height, , in feet of an object above the ground is given by , where is the time in seconds.
  • Find the time it takes the object to strike the ground.
  • Find the maximum height of the object.
  • We have our options. Which one?
    • Graph (inefficient)
    • S.R. Principle (works only w/ Binomials.)
    • Factor (large numbers)
    • Quadratic Formula (versatile)

Solving Example 2, Part 1

  • Given the size of the numbers, it's best to use the Quad Formula to solve.
    • It's very likely they're not clean numbers.

Solving Example 2, Part 2

  • Since a negative time answer is extraneous, we can exclude it. .
  • To find the maximum height, we need the vertex.
    • .

Example 3: Multi-sectioned Area

  • Two rectangular coralls are being made from of fencing. If the rancher wants to maximise the area, what dimensions should be used to make the corrals?
  1. Define Variables
  2. Make formulas

Solving Example 3

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