Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
Convert a quadratic to vertex form
Algebra
CCSS HSF.IF.C.8.ACCSS HSA.SSE.B.3.BEngland: A-level Pure Mathematics
Objective and success criteria
Students will: Convert a quadratic to vertex form.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Completing the square; Quadratic functions in vertex form
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Completing the square; Quadratic functions in vertex form). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write x² + 8x + 7 in the form (x + p)² + q. What is p? → 4Prompt: p is half of the coefficient of x.
- What is the minimum value of f(x) = (x − 1)² − 1? → -1Prompt: The squared term is never negative.
- Find the turning point of y = x² + 6x + 18 by completing the square. Type it like (2, −1). → (−3, 9)Prompt: Write it as (x − h)² + k.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Convert a quadratic to vertex form. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Write y = x² − 2x − 8 in vertex form.
- Step 1: (x − 1)² = x² − 2x + 1
- Step 2: y = (x − 1)² − 9
- Answer: y = (x − 1)² − 9
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Write y = x² + 8x + 11 in vertex form. (y = (x − 4)² − 5 / y = (x + 4)² + 11 / y = (x + 4)² − 5 / y = (x + 8)² − 5) → y = (x + 4)² − 5Prompt: Halve the x coefficient to get the bracket.
- Write y = −2x² + 8x − 12 in vertex form. (y = -2(x − 2)² − 4 / y = -2(x + 2)² − 4 / y = -2(x − 2)² − 12 / y = (x + 4)² − 4) → y = -2(x − 2)² − 4Prompt: Factor −2 out of the x² and x terms first.
You do: independent practice · 7 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Write y = x² − 8x + 5 in vertex form. (y = (x − 4)² + 5 / y = (x + 4)² − 11 / y = (x − 4)² − 11 / y = (x − 8)² − 11) → y = (x − 4)² − 11Prompt: Halve the x coefficient to get the bracket.
- Write y = −x² + 8x − 10 in vertex form. (y = −(x + 4)² + 6 / y = −(x − 4)² + 6 / y = −(x − 4)² − 10 / y = (x + 4)² + 6) → y = −(x − 4)² + 6Prompt: Factor −1 out of the x² and x terms first.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Completing the square.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.
Free lesson plan from eurekami.com/lesson-plan-builder