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Math lesson plan · 9th grade (Year 10 in England) · 45 minutes

Graphs of quadratics: roots, vertex, intercepts

Algebra

CCSS HSF.IF.B.4CCSS HSF.IF.C.7.AEngland: GCSE Foundation AlgebraEngland: GCSE Higher Algebra

Objective and success criteria

Students will: Graphs of quadratics: roots, vertex, intercepts.

  • 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: Solve quadratics by factorising; Graphs of linear equations y = mx + b

Leads to: Completing the square; Transformations of functions; Find the axis of symmetry and vertex of y = ax² + bx + c

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 (Solve quadratics by factorising; Graphs of linear equations y = mx + b). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Solve: x² + 10x + 9 = 0. Give both solutions, separated by a comma. → x = -9 or x = -1Prompt: Factorise: find two numbers that multiply to 9 and add to 10.
  2. Solve: x² − 7x = 0. Give both solutions, separated by a comma. → x = 0 or x = 7Prompt: Take out the common factor x.
  3. Solve: x² + 15x + 54 = 0. Give both solutions, separated by a comma. → x = -9 or x = -6Prompt: Factorise: find two numbers that multiply to 54 and add to 15.

Hook · 5 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Graphs of quadratics: roots, vertex, intercepts. 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: Does the parabola y = −(x + 4)² − 6 have a maximum or a minimum point?
  • Step 1: Negative coefficient: opens down, so a maximum.
  • Answer: Maximum
  • 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.
  1. Does the parabola y = −(x − 1)² − 3 have a maximum or a minimum point? (Maximum / Minimum) → MaximumPrompt: Look at the sign of the x² coefficient.
  2. Does the parabola y = 2(x − 1)² − 2 have a maximum or a minimum point? (Maximum / Minimum) → MinimumPrompt: Look at the sign of the x² coefficient.

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.
  1. Does the parabola y = −(x − 1)² + 8 have a maximum or a minimum point? (Maximum / Minimum) → MaximumPrompt: Look at the sign of the x² coefficient.
  2. Does the parabola y = (x + 3)² − 5 have a maximum or a minimum point? (Maximum / Minimum) → MinimumPrompt: Look at the sign of the x² coefficient.

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: Solve quadratics by factorising.
  • 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: Completing the square; Transformations of functions; Find the axis of symmetry and vertex of y = ax² + bx + c.
  • 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

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Graphs of quadratics: roots, vertex, intercepts

Name

Date

Score/ 8

  1. Question 1

    Find the x-intercepts (roots) of y = x² − 4. Separate them with a comma.

    xy−10−8−6−4−2246810−40−32−24−16−88162432400(2, 0)(−2, 0)(0, −4)

    x =

  2. Question 2

    Does the parabola y = 2(x − 1)² + 8 have a maximum or a minimum point?

    • A. Maximum
    • B. Minimum

  3. Question 3

    Find the x-intercepts (roots) of y = x² − 6x + 8. Separate them with a comma.

    xy−10−8−6−4−2246810−40−32−24−16−88162432400(2, 0)(4, 0)(0, 8)

    x =

  4. Question 4

    Does the parabola y = −2(x − 5)² + 7 have a maximum or a minimum point?

    • A. Maximum
    • B. Minimum

  5. Question 5

    Where does y = x² − x − 12 cross the y-axis? Give the y-value.

    xy−10−8−6−4−2246810−40−32−24−16−88162432400(−3, 0)(4, 0)(0, −12)

    Answer

  6. Question 6

    Does the parabola y = −2(x + 3)² + 4 have a maximum or a minimum point?

    • A. Maximum
    • B. Minimum

  7. Question 7

    Where does y = x² + 7x + 10 cross the y-axis? Give the y-value.

    xy−10−8−6−4−2246810−40−32−24−16−88162432400(−2, 0)(−5, 0)(0, 10)

    Answer

  8. Question 8

    Does the parabola y = 2(x + 5)² − 6 have a maximum or a minimum point?

    • A. Maximum
    • B. Minimum

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Answer key: Graphs of quadratics: roots, vertex, intercepts

  1. 1. x = -2 or x = 2

  2. 2. B. Minimum

  3. 3. x = 2 or x = 4

  4. 4. A. Maximum

  5. 5. -12

  6. 6. A. Maximum

  7. 7. 10

  8. 8. B. Minimum