Solving quadratic equations by completing the square
I can solve quadratic equations algebraically by completing the square.
Solving quadratic equations by completing the square
I can solve quadratic equations algebraically by completing the square.
These resources will be removed by end of Summer Term 2025.
Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.
These resources were created for remote use during the pandemic and are not designed for classroom teaching.
Lesson details
Key learning points
- There are other methods to find the solutions of a quadratic equation.
- One of these methods is called completing the square.
- By representing this with a model, you can see why it has this name.
- Completing the square is useful when the quadratic cannot be easily factorised.
- The square root of a number can be positive or negative.
Keywords
Completing the square - Completing the square is the process of rearranging an expression of the form ax^2 + bx + c into an equivalent expression of the form a(x + p)^2 + q
Common misconception
That we subtract the constant squared when the constant in the bracket is positive and add the constant squared when the constant in the bracket is negative.
Squaring a negative value gives a positive value. Whether the constant in the bracket is positive or negative, the square of the constant must always be subtracted. This can be made clearer with algebra tiles or area models.
To help you plan your year 10 maths lesson on: Solving quadratic equations by completing the square, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Solving quadratic equations by completing the square, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Algebraic manipulation unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
Prior knowledge starter quiz
6 Questions
