Home›Lesson Plans›Mathematics›Algebra II · Grade 11

Solving Quadratics: Factoring & the Formula

Students learn to solve quadratic equations — finding the x-values where a parabola crosses zero — by factoring when possible and by the quadratic formula when it isn’t, the workhorse method that solves every quadratic.

Grade 11Quadratics50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Solve quadratics by factoring.
  • ✓Use the zero product property.
  • ✓Apply the quadratic formula.
  • ✓Interpret roots as x-intercepts.
Essential Question

A parabola’s roots are where it crosses the x-axis — the solutions to ax² + bx + c = 0. How do you find them, even when the equation won’t factor neatly?

0
Lesson Phases
0
Vocabulary Terms
0
Standards Aligned
0
Interactive Task
Model · Interactive Tool

Solve the Quadratic

Project each item and have students solve. The tool shows factoring and the quadratic formula — the method that always works.

🧮 Solve each quadratic equationTry it
Solve each quadratic equation.
The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Where It Hits Zero

5 min

A parabola’s roots are where y = 0 — how do we find them?

👩‍🏫 Teacher Moves

  • Show a parabola crossing zero.
  • Ask for the x-values.
  • Set the goal: solving quadratics.

🎒 Student Actions

  • See the roots.
  • Wonder how.
  • Predict the method.
2

I Do — Factor & the Formula

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Factor and use zero product.
  • Introduce the quadratic formula.
  • Solve a non-factorable one.

🎒 Student Actions

  • Factor one.
  • Learn the formula.
  • Solve a hard one.
3

We Do — Solve Together

13 min

Class uses Solve the Quadratic.

👩‍🏫 Teacher Moves

  • Work each problem.
  • Pick factoring or formula.
  • Check the roots.

🎒 Student Actions

  • Solve each.
  • Pick a method.
  • Check roots.
4

You Do — On Your Own

12 min

Students solve quadratics.

👩‍🏫 Teacher Moves

  • Assign factorable and not.
  • Use the best method.
  • Interpret the roots.

🎒 Student Actions

  • Solve them.
  • Choose a method.
  • Interpret roots.
5

Close — Close

5 min

One quadratic.

👩‍🏫 Teacher Moves

  • Give a quadratic to solve.
  • Show the method.
  • Hand out the exit ticket.

🎒 Student Actions

  • Solve it.
  • Show the work.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School: Algebra II).

CCSS
A-REI.4

Solve quadratic equations in one variable.

CCSS
A-REI.4b

Solve quadratics by inspection, factoring, completing the square, and the quadratic formula.

CCSS
A-SSE.3a

Factor a quadratic to reveal the zeros of the function.

CCSS
N-CN.7

Solve quadratic equations with complex solutions.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Factoring steps card.
  • Sentence frame: “Set each factor to ___.”
  • Provide the quadratic formula.

Support & Access

IEP / 504
  • Start with simple factoring.
  • Provide the formula on a card.
  • Use a calculator for roots.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Solve by completing the square.
  • Find complex roots.
  • Use the discriminant to predict roots.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻Solve the Quadratic
  • 🧮Calculators
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

quadratic equationan equation with an x² termroota solution; an x-interceptfactorto write as a productzero product propertyif a product is 0, a factor is 0quadratic formulax = (−b ± √(b²−4ac))/2adiscriminantb² − 4accompleting the squarea method to solve quadraticsparabolathe graph of a quadratic
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Solve by factoring: x² + 7x + 12 = 0.
x = −3 and x = −4 (from (x+3)(x+4) = 0).
QUESTION 2
When would you use the quadratic formula instead of factoring?
When the quadratic does not factor neatly — the formula solves any quadratic.
QUESTION 3
What do the solutions (roots) of a quadratic represent on its graph?
The x-intercepts — where the parabola crosses the x-axis.

Going deeper? The discriminant.

Have students use the discriminant (b² − 4ac) to predict whether a quadratic has two real, one real, or two complex solutions — before solving. A printable quadratics sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Solving Quadratic EquationsFlip
Card 1
Term
Tap to flip →
Meaning
0

Nice work!

Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Solving Quadratic EquationsQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Solving Quadratic EquationsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: completing the square, discriminant, factor, parabola, quadratic equation, quadratic formula, root, zero product property
  1. if a product is 0, a factor is 0
  2. the graph of a quadratic
  3. b² − 4ac
  4. a solution; an x-intercept
  5. x = (−b ± √(b²−4ac))/2a
  6. a method to solve quadratics
  7. to write as a product
  8. an equation with an x² term

Part B · Show what you learned

  1. Solve by factoring: x² + 7x + 12 = 0.
  2. When would you use the quadratic formula instead of factoring?
  3. What do the solutions (roots) of a quadratic represent on its graph?
Answer key — Part A: 1) zero product property · 2) parabola · 3) discriminant · 4) root · 5) quadratic formula · 6) completing the square · 7) factor · 8) quadratic equation
Part B: 1) x = −3 and x = −4 (from (x+3)(x+4) = 0). 2) When the quadratic does not factor neatly — the formula solves any quadratic. 3) The x-intercepts — where the parabola crosses the x-axis.