Quadratic Graphing Fun

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Date:

WALT & Success Criteria

WALT: We are learning to plot quadratic graphs from a table of values and connect them to make a picture.

Success criteria: I can

- plot given (x, y) points accurately, - draw a smooth parabola through the points, - label the vertex and axis of symmetry on at least one parabola.

Differentiation:

Support: use grid paper and plot fewer points (three). Challenge: find the equation from the plotted points.

Extension: For advanced learners, try shifting or stretching one equation to make a new wing or arc and provide its table of values.

Dyslexia-friendly reading options: Short sentences, bold key words (plot, label, smooth). Work with a partner and use coloured pens for different parabolas to help follow lines.

Graphing Activity: Create the Picture

1. Butterfly — Left wing.
Equation: y = -0.5x² + 4
Table of values: (-4, -4), (-2, 2), (0, 4), (2, 2), (4, -4).
Plot these points and draw a smooth parabola. Label the vertex.

2. Butterfly — Right wing (shifted right).
Equation: y = -0.5(x - 6)² + 4
Table of values: (2, -4), (4, 2), (6, 4), (8, 2), (10, -4).
Plot and join smoothly to match the left wing. Label its vertex and axis of symmetry.

3. Rainbow — Outer arc.
Equation: y = -0.05x² + 6
Table of values: (-10, 1), (-5, 4.75), (0, 6), (5, 4.75), (10, 1).
Plot and draw a smooth arc.

4. Rainbow — Inner arc.
Equation: y = -0.03x² + 5
Table of values: (-10, 2), (-5, 4.25), (0, 5), (5, 4.25), (10, 2).
Plot this inside the outer arc to create a layered rainbow.

5. Bridge — Main arch.
Equation: y = -0.2x² + 3
Table of values: (-6, -4.2), (-3, 1.2), (0, 3), (3, 1.2), (6, -4.2).
Plot and draw one smooth arch to represent a bridge.

6. Smiling face — Mouth (U-shape).
Equation: y = 0.2x² - 2
Table of values: (-3, -0.2), (-1, -1.8), (0, -2), (1, -1.8), (3, -0.2).
Plot and draw a gentle smile. Label the lowest point (vertex).

7. Fireworks — Central burst (narrow arcs).
Equation: y = -1x² + 6
Table of values: (-2, 2), (-1, 5), (0, 6), (1, 5), (2, 2).
Plot these points and draw a sharp, narrow parabola. Repeat with different colours for extra bursts if you like.

8. Reflection: Choose one parabola you plotted. State its vertex and axis of symmetry (give exact coordinates / equation). Explain in one or two sentences how you found the vertex.