Quadratic Graphs
Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions
Lesson
Set out your lesson
“Quadratic Graphs means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Coordinate grid (−5 to 5)
- Pencil
Extra for the adult
Worked example. For y=x², when x=2, y=4. The points form a U-shaped curve.
Optional challenge. For Quadratic Graphs, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Quadratic Graphs, not mastery.
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Teaching approaches
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1 approach
Quadratic Graphs means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Coordinate grid (−5 to 5); Pencil. 1. Say the goal of Quadratic Graphs in plain words once. 2. Adult plots y=x² for x=−2,−1,0,1,2 and sketches the curve. 3. Child plots three quadratic tables and sketches each curve. 4. Fresh check: one fresh y=x² table point. Record and stop. Done: three plotted quadratics with a clear vertex note. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Practice this concept
Start practiceQuadratic Graphs practice
Practice key ideas from Quadratic Graphs.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Comparing two different pizzas
Before you open · source notes
Comparing two different pizzas supports quadratic graphs. Not every worksheet pack.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to explain one step of “Comparing two different pizzas” in their own words.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Comparing two different pizzas.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- Explain why x² produces a U-shaped curve rather than a straight line
- Plot a simple quadratic such as y = x² − 4 from a table of values
- Read approximate solutions from a quadratic graph (e.g., where y = 0)
“Can your child recognise that an equation like y = x² produces a curved graph rather than a straight line, and use a plotted curve to estimate values?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Algebra
- Age range
- Ages 13–14
Standards