C2.11 Sketching curves
- Syllabus
- 0580–2028–2029
- Topic
- C2.11
- Level
- Core
Learning objectives
Sketch linear and quadratic graphs from their key features
A sketch shows the correct graph family and its defining features without requiring a full table of values or exact plotting. Mark roots and intercepts clearly, then draw the shape consistently with them.
| Feature | Linear graph | Quadratic graph |
|---|---|---|
| overall shape | one straight line | one smooth parabola |
| roots | where the line crosses the x-axis | where the curve crosses or touches the x-axis |
| symmetry | not required | a vertical line; paired points at the same height lie equally far from it |
| direction | rises or falls at a constant rate | opens upwards or downwards |
For y=−2x+4, the y-intercept is (0,4) and the root is (2,0). Mark these points and join them with one straight falling line. A linear sketch must not bend.
For y=(x+1)(x−5), the roots are x=−1 and x=5. Their midpoint is (−1+5)/2=2, so the line of symmetry is x=2. Since the coefficient of x2 is positive, draw a smooth upward-opening curve through both roots, mirrored about x=2. The y-intercept is (0,−5), which helps place the curve.
To interpret a quadratic graph, read each root as an x-value where y=0. Read its symmetry line as x=k: points with equal y-values occur at equal horizontal distances on either side of x=k. If the curve only touches the x-axis, that root lies on the symmetry line.
Do not calculate or label an exact turning point unless the question supplies enough information and asks for it; C2.11 requires roots and symmetry, not turning-point knowledge. A sketch still needs the correct intercepts, symmetry and opening direction.