M4.10.8 For the adult
Solving with graphs and trials
Two graphs cross at a point. What does that point have to do with solving an equation?
What this chapter teaches
To solve f(x) = g(x), draw both graphs and read the x values where they cross. A root is where a graph meets the x axis. If f has no break and changes sign between two numbers, there is a root between them, and trying values in smaller steps closes in on it. Trying the middle value shows how to round.
Three questions to ask
There is no one right wording. Listen for the idea.
- How do you solve x² = x + 2 using two graphs, and why do you read the x values?
- How can you tell that x³ + x − 3 has a root between 1 and 2 without drawing it?
- Why does a change of sign for 1/x not give a root?
After the chapter, the learner can
- Solve an equation by finding where two graphs meet
- Find a root between two numbers by trying values
What they copy into their notebook
Solve f(x) = g(x): read the x values where the graphs cross. Roots: where f changes sign, if there is no break. Narrow the gap by trying values.