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Math lesson plan · 9th grade (Year 10 in England) · 60 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 · 6 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 + 3x − 18 = 0. Give both solutions, separated by a comma. → x = -6 or x = 3Prompt: Factorise: find two numbers that multiply to −18 and add to 3.
  2. Solve: x² + 8x = 0. Give both solutions, separated by a comma. → x = -8 or x = 0Prompt: Take out the common factor x.
  3. Solve: x² + 4x − 5 = 0. Give both solutions, separated by a comma. → x = -5 or x = 1Prompt: Factorise: find two numbers that multiply to −5 and add to 4.

Hook · 6 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 · 12 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 · 12 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 = 2(x + 5)² + 4 have a maximum or a minimum point? (Maximum / Minimum) → MinimumPrompt: Look at the sign of the x² coefficient.
  2. Does the parabola y = −2(x + 2)² + 5 have a maximum or a minimum point? (Maximum / Minimum) → MaximumPrompt: Look at the sign of the x² coefficient.

You do: independent practice · 17 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 · 7 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 + 4)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 = −(x + 2)² − 6 have a maximum or a minimum point? (Maximum / Minimum) → MaximumPrompt: 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

eurekami

Graphs of quadratics: roots, vertex, intercepts

Name

Date

Score/ 8

  1. Question 1

    What is the x-coordinate of the vertex (turning point) of y = x² + 3x − 18?

    xy−10−8−6−4−2246810−40−32−24−16−88162432400(−6, 0)(3, 0)(0, −18)

    Answer

  2. Question 2

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

    • A. Maximum
    • B. Minimum

  3. Question 3

    What is the x-coordinate of the vertex (turning point) of y = x² + 7x + 10?

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

    Answer

  4. Question 4

    Does the parabola y = −(x + 3)² − 7 have a maximum or a minimum point?

    • A. Maximum
    • B. Minimum

  5. Question 5

    Find the x-intercepts (roots) of y = x² + 6x + 5. Separate them with a comma.

    xy−10−8−6−4−2246810−40−32−24−16−88162432400(−1, 0)(−5, 0)(0, 5)

    x =

  6. Question 6

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

    • A. Maximum
    • B. Minimum

  7. Question 7

    What is the x-coordinate of the vertex (turning point) of y = x² + 6x + 5?

    xy−10−8−6−4−2246810−40−32−24−16−88162432400(−5, 0)(−1, 0)(0, 5)

    Answer

  8. Question 8

    Does the parabola y = −2(x + 1)² + 2 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. -1.5

  2. 2. A. Maximum

  3. 3. -3.5

  4. 4. A. Maximum

  5. 5. x = -5 or x = -1

  6. 6. B. Minimum

  7. 7. -3

  8. 8. A. Maximum