CCSS.MATH.CONTENT.HSA.REI.B.4✓ Connecticut State Department of Education AlignedAcademic Year 2026–27
Solving Quadratic Equations by Factoring & Formula
Master solving quadratic equations (ax² + bx + c = 0) using factoring, completing the square, and the universal quadratic formula.
Why It Matters:Essential for projectile kinematics in physics, profit maximization curves in economics, and rendering parabolic paths in 3D gaming.
Curated Video Instruction
● Verified Active EmbedSTEP-BY-STEP PROOF
Worked Example
Solve for x: x² - 5x + 6 = 0
1
Identify factors of +6 that sum to -5
(-2) * (-3) = 6 and (-2) + (-3) = -5
Factoring trinomials of form x² + bx + c.
2
Rewrite as binomial factors
(x - 2)(x - 3) = 0
Apply zero-product property.
3
Set each factor to zero
x - 2 = 0 or x - 3 = 0
A product is zero if either factor equals zero.
4
Solve for x
x = 2 or x = 3
Two real roots satisfy the quadratic.
✓Verification Check
Test x = 2: (2)² - 5(2) + 6 = 4 - 10 + 6 = 0.
4 - 10 + 6 = 0
•
0 = 0 (Verified)
⚠️ Common Pitfalls & Misconceptions
Forgetting the ± symbol when taking square roots
✗ x² = 25 => x = 5 only✓ x² = 25 => x = ±5 (both 5 and -5)
Every non-zero real number has both a positive and negative square root.
INTERACTIVE DRILLS
Guided Practice
Practice Question1 of 1
Step-by-step Feedback
What are the solutions to x² - 7x + 12 = 0?
MASTERY BENCHMARK
Official Assessment Quiz
Formal Assessment
Solving Quadratic Equations by Factoring & Formula
Passing Criteria:70% or higher
Question 1 of 1
In the quadratic formula, what does the discriminant (b² - 4ac) indicate when greater than zero?
Education to Career Navigation
Where This Lesson Leads
Aerospace Guidance Engineers and Quantitative Traders use quadratic optimization algorithms continuously.