LEARN · EXPLAIN · REVISE
Read the idea, work independently, then explain what changed.
高一必修 第一册(A版).pdf · 2.3 · PDF 57 / printed page 50
Revisit first: Vertex form and completing the square
TOPIC 01
Choose a root method, then check reality, location and the original domain.
Use one hint at a time. A correction explains what changed, not just the final answer.
Scope: JM01 / JM02
Working and explanation
BUILD THE REASONING
Set the squared base to zero.
There is one distinct input.
B: one distinct real root.
Checks and common pitfalls: Repeated multiplicity is not a second input.
Think first. Reveal a hint when the class is ready.
| Minutes | Focus | Teaching and student action |
|---|---|---|
| 5 | Count and cancel | Contrast repeated roots and lost zeros with diagnostics. |
| 8 | Derive Δ | Derive the squared equation, marking a≠0. |
| 10 | Method sorting | Pairs sort root-value, sum and intersection tasks. |
| 12 | Case audit | Groups solve the k problem and audit the linear branch. |
| 5 | Repair a claim | Use a counterexample to separate positive roots from real roots. |
Full: k=1 and k=2; partial: only Δ=0.
Full rational answer: −2 with x≠2; incorrect: ±2.
