math · Grade 9
Algebra 1: Solving Quadratic Equations & The Quadratic Formula
Master factoring trinomials, evaluating the discriminant, and applying the quadratic formula with complete worked step-by-step solutions.
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Learning goals
- Solve quadratic equations ax² + bx + c = 0 by factoring and zero-product property
- Calculate and interpret the discriminant b² - 4ac to determine the number and nature of real solutions
- Apply the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) to find exact solutions
Before you begin
Expand and factor simple expressions and understand an equation's solutions.
Age and grade do not measure readiness. Adjust reading or adult support to preserve the intended learning goal.
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1. Practice
Practice previewAlgebra 1: Solving Quadratic Equations & The Quadratic Formula
Practice · Independent · 15 min
Master factoring trinomials, evaluating the discriminant, and applying the quadratic formula with complete worked step-by-step solutions.
Teaching and response guide
- Model the target skill: solve quadratic equations ax² + bx + c = 0 by factoring and zero-product property. Use the first task as a guided example before asking for an independent response.
- Check readiness first: Expand and factor simple expressions and understand an equation's solutions.
- Discuss an incorrect response using this distinction: Setting each factor to zero is valid when their product equals zero; a nonzero right side requires another step.
Watch for: Setting each factor to zero is valid when their product equals zero; a nonzero right side requires another step.
Check the answer criteria for each task. A supported explanation may have more than one acceptable response. These activities offer evidence to discuss; completing a sheet alone does not establish mastery.
Possible next goals
Choose the next unit when its prerequisites fit your learner.