Study Guide — HSA.REI.B.4
Solve quadratic equations in one variable
Solve equations and inequalities and justify each step.
What this standard means
- Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive the quadratic formula from this form.
- Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
- Apply solve quadratic equations in one variable with models and explanation
- Solves linear and quadratic equations
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Do the same operation to both sides 2. Graph solutions on a number line 3. Check solutions by substitution
_See printable PDF for diagram._
Common mistakes
- Dividing by zero
- Reversing inequality when multiplying by negative
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for HSA.REI.B.4.
- [ ] Solves linear and quadratic equations
- [ ] Solves inequalities and graphs solutions
- [ ] Justifies steps algebraically
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors