Key Idea: Reading a graph means naming its landmarks — intercepts, turning points and asymptotes — and finding where two graphs meet. It runs through both papers: by hand on Paper 1, on the GDC for Paper 2.
🗺️ The key-features menu
Maximum value wants a y-coordinate; maximum point wants coordinates (x, y); where the maximum occurs wants the x-coordinate. The words zero, root and x-intercept all mean the same thing — set y = 0.
Where graphs cross, that point lies on both curves, so its x makes f(x) = g(x). On Paper 1, set f(x) = g(x), move everything to one side, solve, then substitute each x back for its y. On Paper 2, graph both and use intersect. Solving f(x) = k is just meeting the line y = k (k = 0 gives the x-intercepts).
✏️ IB-style worked examples
IB-style question — find the intercepts
Find the intercepts of f(x) = (x − 3)(x + 5).
Step by step:
x-intercepts (zeros): set each factor to 0.
y-intercept: set x = 0.
Final answer:
Zeros at x = 3 and x = −5; y-intercept (0, −15).
IB-style question — state the minimum point and value
State the minimum point and minimum value of f(x) = (x − 4)² − 7.
Step by step:
Vertex form a(x − h)² + k turns at (h, k).
a = 1 > 0, so it opens up — it's a minimum.
Final answer:
Minimum point (4, −7); minimum value −7.
IB-style question — find where two graphs meet (Paper 1)
Find where y = x² + 2 meets y = 3x + 2, without a calculator.
Step by step:
Set the two equal.
Bring everything to one side.
Factor and solve.
Substitute each x back (use y = 3x + 2) for its y.
Final answer:
They meet at (0, 2) and (3, 11).
Important: Solving f(x) = g(x) (or f(x) = k) gives the x-values only. The question almost always wants points, so substitute each x back to get its y. And check for every crossing — a parabola meets a line at up to two points.
Tap each card to reveal the answer.
Exam Tips
- Match the wording: value → y-coordinate, point → (x, y), where → x-coordinate.
- Zero = root = x-intercept (set y = 0); y-intercept comes from x = 0.
- Vertical asymptote: denominator = 0. Horizontal asymptote: what y levels off to as x → ±∞.
- Intersections solve f(x) = g(x); f(x) = k meets the line y = k. Always finish with the y-coordinate.
- Paper 2: CALC menu — 2:zero, 3:minimum, 4:maximum, 5:intersect — and check for more than one crossing.