Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
Quadratic functions in vertex form
Algebra
CCSS HSF.IF.C.8.ACCSS HSF.IF.B.4
Objective and success criteria
Students will: Quadratic functions in 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
Leads to: Convert a quadratic to vertex form
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). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write x² − 12x + 21 in the form (x + p)² + q. What is q? → -15Prompt: p is half of the coefficient of x.
- Find the turning point of y = x² − 2x + 11 by completing the square. Type it like (2, −1). → (1, 10)Prompt: Write it as (x − h)² + k.
- Write x² − 8x + 17 in the form (x + p)² + q. What is p? → -4Prompt: p is half of the coefficient of x.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Quadratic functions in 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: What is the minimum value of f(x) = (x − 3)² + 6?
- Step 1: At x = 3 the bracket is 0, so f = 6.
- Answer: 6
- 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.
- What is the minimum value of f(x) = 2(x + 2)² + 6? → 6Prompt: The squared term is never negative.
- What is the x-coordinate of the vertex of y = −x² + 8x − 16? → 4Prompt: x = −b/(2a).
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.
- What is the x-coordinate of the vertex of y = −x² − 8x − 12? → -4Prompt: x = −b/(2a).
- What is the maximum value of f(x) = −2(x + 3)² − 5? → -5Prompt: The squared term is never negative.
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
- Move on to: Convert a quadratic to vertex form.
- 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