Transformations of Graphs
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Transformations of Graphs — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionCombining Multiple TransformationsConcept Practice
4 marks~6 minCriterion A
A drone follows a flight path modelled by f(x)=x2f(x) = x^2, where xx is horizontal distance (metres) and f(x)f(x) is height (metres). An adjusted path is modelled by g(x)=(x+3)2−5g(x) = (x+3)^2 - 5.

A safety regulation states that the drone must remain at or above −4-4 metres relative to the launch reference height.
a
State the coordinates of the vertex of g(x)g(x). [1]
b
Explain how the graph of g(x)g(x) is obtained from the graph of f(x)f(x) through translations. [2]
c
Evaluate g(−2)g(-2) and justify whether the drone satisfies the safety regulation at x=−2x = -2. [1]
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Solutions

2QuestionStretching and Compressing GraphsAssessment Practice
4 marks~6 minCriterion D
A civil engineer models the vertical sag of a suspension bridge cable using

y=0.005x2y = 0.005x^2

where yy is the vertical sag in metres and xx is the horizontal distance in metres from the lowest point.
a
When the load increases by 20%, the engineer applies a vertical stretch by a factor of 1.2. Determine the new function. [1]
b
The bridge has a main span of 400 m, so xx ranges from −200-200 to 200200. Calculate the maximum sag predicted by the new model. [1]
c
The engineer claims the quadratic model is sufficient for all design decisions. Critique this claim, referring to at least two real-world factors not captured by the model. [2]
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Solutions

3QuestionCombining Multiple TransformationsConcept Practice
2 marks~3 minCriterion B
A parabolic solar reflector dish is repositioned on a tracking mount. Its cross-section is modelled by g(x)=(x−h)2+kg(x) = (x - h)^2 + k, where hh is the horizontal adjustment (in metres) and kk is the minimum height (in metres) above the base frame.

Four positioning configurations are recorded:

hh: 2, 4, −1, −32,\ 4,\ -1,\ -3

kk: 1, 3, 5, 21,\ 3,\ 5,\ 2

Analyse the relationship between hh, kk, and the vertex of gg across all four configurations, and state the general rule for the vertex coordinates of g(x)=(x−h)2+kg(x) = (x - h)^2 + k. [2]

Solutions

4QuestionDescribing Graph Changes AlgebraicallyAssessment Practice
5 marks~8 minCriterion C
The diagram shows the graphs of f(x)=x2f(x) = x^2 and its image g(x)g(x) after two transformations applied in order: a vertical stretch by scale factor 33, followed by a vertical translation of −4-4 units.
a
Write down the equation of g(x)g(x). [1]
b
Find the coordinates of the vertex of g(x)g(x) and state the range of g(x)g(x). [2]
c
The graph of g(x)g(x) is translated by (p0)\begin{pmatrix} p \\ 0 \end{pmatrix} to give the graph of h(x)h(x), where h(x)=3x2−12x+8h(x) = 3x^2 - 12x + 8. Justify whether p=2p = 2 is the correct value for this translation vector. [2]
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Solutions

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