YEAR 9 MATHEMATICS · PARABOLAS
Interactive teacher demonstration · Dilation, reflection and translation
I DO · Start here

Meet the parabola

What do you notice about this U-shaped curve?

YEAR 9 · 15-MINUTE DEMO
y = x²
I DO → WE DO → YOU DOKeyboard: 1–5 sections · ←/→ change a · F full screen
Teacher prompts and a 15-minute lesson route
  1. 2 minutes — Parent parabola: Ask students to spot the vertex, symmetry and U-shape. Compare x = −2 and x = +2.
  2. 4 minutes — Dilation: Set a = 1, 2, then 0.5. Students predict wider or narrower before the curve moves. Emphasise that dilation multiplies every y-value.
  3. 3 minutes — Reflection: Switch a from positive to negative. Ask: “Why did it turn upside down?” Check the vertex remains at (0, 0).
  4. 3 minutes — Move the vertex (optional extension): Change h and k or drag the orange vertex. Point out this is translation, not dilation.
  5. 3 minutes — Quick check: Use mini-whiteboards, hide the answer, then reveal the reasoning. Have students justify their choices.

Mathematical note: y = a(x − h)² + k. When |a| > 1 the graph is vertically stretched (narrower); when 0 < |a| < 1 it is compressed (wider). Negative a reflects the graph in the x-axis. h and k translate the graph, leaving its shape unchanged. All graphs are calculated numerically and drawn as SVG paths, not generated by AI.