Quadratic equations – Grade 9 math lesson
Lesson 11 of 17 in the Grade 9 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 9 (ages 14–15) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 9 (ages 14–15)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “What does the discriminant tell you before you solve?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Only giving one solution. Set each factor to zero: there are usually two.
- Getting the signs wrong in the formula. Write a, b and c down with their signs first.
Tip for home: Talk about the path of a thrown ball as a quadratic curve.
What your child will learn
Learning goal: solve quadratic equations by factoring, the quadratic formula and completing the square.
Success looks like
- I can solve by factorising.
- I can use the quadratic formula.
- I can complete the square.
Key words
- quadratic
- with x² as the highest power
- root
- a solution of the equation
- discriminant
- b² − 4ac, which tells how many solutions
- vertex
- the highest or lowest point of the curve
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use a graph-plotting app or table of values to see where y = x² − 4 crosses the x-axis.
The big ideas (for the adult)
A quadratic equation has an x² term. Rearrange to = 0, factor, then set each factor to zero: (x − 2)(x + 5) = 0 gives x = 2 or x = −5.
When it will not factorise, use the quadratic formula: x = (−b ± √(b² − 4ac)) / 2a.
Completing the square writes x² + bx + c as (x + b/2)² + k, which also shows the turning point of the graph.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 9 math lessons
- Rates and unit rates
- Converting units
- Upper and lower bounds
- Simplifying expressions
- Expanding expressions
- Factoring
- Solving equations
- Inequalities
- Rearranging formulas
- Systems of equations
- Identities and proof
- Arithmetic and geometric sequences
- Linear functions and slope
- Functions
- Graphing functions
- Exponential functions
Curriculum
Common Core State Standards HSA.APR.B.3: “Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.”
Common Core State Standards HSA.REI.B.4.b: “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.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.