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.
13 marks
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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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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For the quadratic y = x² − 6x + 5, state the interval on which it is decreasing.
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For y = −x² + 4x, state the interval on which it is increasing.
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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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A graph falls from left to right between x = −1 and x = 4. State whether the function is increasing or decreasing there.
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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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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 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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Use a GDC to find the local minimum of f(x) = x² − 6x + 11.
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Use a GDC to find the local maximum of f(x) = −x² + 4x + 1.
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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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Find the vertex of y = −2x² + 8x using x = −b/(2a).
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State the maximum number of turning points a cubic function can have.
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At a local maximum, does the graph change from increasing to decreasing, or decreasing to increasing?
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A function has a local maximum at (1, 8) and a local minimum at (5, 2). State which turning point is higher.
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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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The function y = 2(x − 3)² + 4 is in vertex form. Write down the coordinates of its turning point.
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The graph of f(x) = −x² + 6x − 5 is shown.
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