Functions & Graphs is one of 9 topics in the Grade 11 Technical Mathematics CAPS syllabus, covered across 3 lessons on Study Vault. Below are real practice questions from this topic with full worked answers.
Sample practice questions
Easy
1. For the parabola y = a(x+p)^2 + q, what does a positive value of a tell you about the shape?
The parabola opens upward (minimum turning point)
The parabola opens downward (maximum turning point)
The parabola is a straight line
The parabola has no turning point
Answer: The parabola opens upward (minimum turning point) — If a > 0, the parabola opens upward, giving a minimum turning point.
Easy
2. State the turning point of y = 2(x-3)^2 + 5.
Answer: (3;5) — The turning point of y=a(x+p)^2+q is (-p;q). Here p=-3, so -p=3, and q=5. Turning point: (3;5).
Medium
3. Which parabola is narrower: y = 5(x-1)^2 + 2 or y = 0.5(x-1)^2 + 2?
y = 5(x-1)^2 + 2
y = 0.5(x-1)^2 + 2
They are the same width
Cannot be determined
Answer: y = 5(x-1)^2 + 2 — A larger size of a (ignoring sign) makes the parabola narrower; 5 is larger than 0.5, so y=5(x-1)^2+2 is narrower.
