Unit 2: Functions
Topic 2.4: Quadratic Functions and Models Questions
Practice 8 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.
14 marks
The graph of f(x) = −x² + 6x − 5 is shown. (a) Find the coordinates of the local maximum. (b) Write down the maximum value of f.
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The graph of f has a local maximum at x = 1 and a local minimum at x = 4. State (a) the interval on which f is increasing, (b) the interval on which f is decreasing.
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f(x) = x² − 4x + 1. (a) Find the vertex. (b) Hence write down the interval on which f is decreasing.
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f(x) = 3 · 2ˣ + 5. (a) Write down the equation of the horizontal asymptote. (b) Write down the range of f.
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The population of a colony is modelled by P(t) = 200 · 0.85ᵗ + 50, where t is the number of years. (a) Write down the equation of the horizontal asymptote of P. (b) Explain what this asymptote represents in context.
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The height of a water jet (in metres) above the ground is modelled by h(t) = −2t² + 8t + 3, where t is time in seconds. (a) Find the maximum height reached. (b) Find the time at which the maximum height is reached.
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Use your GDC to find the local minimum and local maximum of f(x) = x³ − 6x + 2.
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The profit P (in thousands of dollars) from selling n items is given by P(n) = −3n² + 24n − 20. (a) Find the number of items that maximises profit. (b) Find the maximum profit.
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