M4.9.8 For the adult
A line and a curve
The line y = x + 2 and the curve y = x² cross. How do I find where?
What this chapter teaches
To find where a line meets a curve, put the two expressions for y equal, solve the quadratic that gives, then find y from the line. A quadratic inequality is read from the graph of the curve: below the x axis between the roots, above it outside them.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why do you put the two expressions for y equal when you look for a meeting point?
- Why does x² < 9 have an answer with two sides, −3 < x < 3, and not just x < 3?
- How can the number of solutions tell you if a line touches, crosses or misses a curve?
After the chapter, the learner can
- Solve a linear and a quadratic equation together
- Solve a quadratic inequality like x² < 9
What they copy into their notebook
Put the two y values equal, solve, then find y from the line. For x² < 9, x is between −3 and 3. For x² > 9, x is below −3 or above 3.