Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Find the axis of symmetry and vertex of y = ax² + bx + c
Algebra
CCSS HSF.IF.C.7.ACCSS HSF.IF.B.4England: GCSE Higher Algebra
Objective and success criteria
Students will: Find the axis of symmetry and vertex of y = ax² + bx + c.
- 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: Graphs of quadratics: roots, vertex, intercepts
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 · 5 min
- Quick retrieval from earlier learning (Graphs of quadratics: roots, vertex, intercepts). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Does the parabola y = (x + 3)² − 8 have a maximum or a minimum point? (Maximum / Minimum) → MinimumPrompt: Look at the sign of the x² coefficient.
- Does the parabola y = (x − 4)² − 2 have a maximum or a minimum point? (Maximum / Minimum) → MinimumPrompt: Look at the sign of the x² coefficient.
- Does the parabola y = −2(x + 2)² − 6 have a maximum or a minimum point? (Maximum / Minimum) → MaximumPrompt: Look at the sign of the x² coefficient.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find the axis of symmetry and vertex of y = ax² + bx + c. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Find the axis of symmetry of y = −2x² + 16x − 23. Give the value of x.
- Step 1: x = −(16) ÷ (2 × (−2))
- Step 2: x = 4
- Answer: 4
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Find the axis of symmetry of y = −2x² − 24x − 68. Give the value of x. → -6Prompt: The axis of symmetry is x = −b/(2a).
- Find the vertex of y = 3x² + 30x + 70. Type it like (2, −1). → (−5, −5)Prompt: Find x = −b/(2a) first.
You do: independent practice · 10 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 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A drone's height (m) after t seconds is h = −2t² + 16t + 1. What is its maximum height? → 33Prompt: The maximum or minimum is at the vertex.
- Find the vertex of y = −2x² + 20x − 45. Type it like (2, −1). → (5, 5)Prompt: Find x = −b/(2a) 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: Graphs of quadratics: roots, vertex, intercepts.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder