Unit 2: Functions
Topic 2.4: Quadratic Functions and Models Questions
Practice 20 exam-style questions for IB Math AI SL Topic 2.4. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1state3 marks
A graph y = f(x) has a local minimum at (-2, -5) and a local maximum at (3, 7). State the local minimum value, the local maximum value, and the x-values at which each occurs.
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2026
A stock's value, S dollars, t days after a market crash is modelled by
S(t) = 1500e−0.05t + 200
Write down the equation of the horizontal asymptote of the graph of S.
S(t) = 1500e−0.05t + 200
Write down the equation of the horizontal asymptote of the graph of S.
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A curve has a local minimum where it changes from decreasing to increasing, at (4, −7). Write down the coordinates of the local minimum.
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State the maximum number of turning points a cubic function can have.
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2026
Consider the function
g(x) = 5x + 8/x²
Write down the equation of the vertical asymptote of the graph of g.
g(x) = 5x + 8/x²
Write down the equation of the vertical asymptote of the graph of g.
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2026
A tea cools so that its temperature T °C after t minutes is modelled by
T(t) = 65e−0.08t + 21
The graph of T has a horizontal asymptote.
Write down the equation of the horizontal asymptote.
T(t) = 65e−0.08t + 21
The graph of T has a horizontal asymptote.
Write down the equation of the horizontal asymptote.
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Find the coordinates of the vertex of y = x² − 8x + 3 using the formula x = −b/(2a).
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The graph of a function has a local maximum at the point where it changes from increasing to decreasing. The point is (−2, 9). Write down the coordinates of the local maximum.
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A curve rises as x increases from 2 to 8. State whether the function is increasing or decreasing on this interval.
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Use a GDC to find the local maximum of f(x) = −x² + 4x + 1.
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A graph y = f(x) has a local maximum at x = 2 and a local minimum at x = 5. State the interval(s) on which f is increasing and the interval(s) on which f is decreasing. Assume f is defined for all real x.
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2026
Consider the function
f(x) = 7/x + 3/x²
Write down the equation of the vertical asymptote of the graph of f.
f(x) = 7/x + 3/x²
Write down the equation of the vertical asymptote of the graph of f.
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The graph of f(x) = −x² + 6x − 5 is shown.
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2026
Consider the function
f(x) = 4x² + 8/x, for x ≠ 0
State the equation of the vertical asymptote of the graph of f.
f(x) = 4x² + 8/x, for x ≠ 0
State the equation of the vertical asymptote of the graph of f.
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Use your GDC to find the coordinates of the local maximum of f(x) = -x² + 6x + 2.
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For y = −x² + 4x, state the interval on which it is increasing.
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Use a GDC to find the local minimum of f(x) = x² − 6x + 11.
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At a local maximum, does the graph change from increasing to decreasing, or decreasing to increasing?
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Find the vertex of y = −2x² + 8x using x = −b/(2a).
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2026
A population of fish in a pond, P, t months after a chemical spill is modelled by
P(t) = 1800e−0.12t + 250
Write down the long-term population the model predicts.
P(t) = 1800e−0.12t + 250
Write down the long-term population the model predicts.
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