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?
- Define Variables
- Make formulas