Grade 11 · CAPS-aligned
Grade 11 Functions — Quadratics, Hyperbolas & Exponentials
Sketch them, read them, and answer the 25 marks they're worth in your paper.
Functions are a quarter of your Grade 11 Paper 1. The skill isn't drawing pretty graphs — it's reading them and answering transformation questions. Three function families dominate: quadratic, hyperbola, and exponential.
Why most learners find this hard
Each function has its own rules for shape, intercepts, and asymptotes. Mixing them up costs 5–6 marks per question. Build a one-page cheat sheet and refer to it for every practice question until you stop checking.
What you'll learn
- Standard forms and shape: y = ax² + bx + c, y = a/(x−p) + q, y = a·bˣ + q
- Finding x- and y-intercepts and turning points
- Identifying asymptotes (vertical and horizontal)
- Effect of a, p, and q on shape and position
- Reading values directly off a sketched graph
Worked example
Find the turning point of y = 2x² − 8x + 3.
- 1x-coordinate of the turning point: x = −b / (2a) = −(−8) / (2·2) = 2
- 2Substitute into the equation: y = 2(2)² − 8(2) + 3 = 8 − 16 + 3 = −5
- 3Turning point is (2, −5)
Answer: (2, −5)
Exam tips
- Draw a quick rough sketch even when not asked — it stops sign mistakes.
- Always state the equation of an asymptote, not just its value.
- When a graph is transformed, do shifts last (after stretches/reflections).
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