AQA · Mathematics · 8300
GCSE Maths: Types of graph: cubics
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Types of graph: cubics (Corbettmaths Video 344), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is the general shape of the graph y = x³?
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An S-shaped curve that passes through the origin, increasing from bottom-left to top-right.
If a point on y = x³ has x-coordinate −3, what is its y-coordinate?
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−27 (since (−3)³ = −27)
How does the graph of y = −x³ differ from y = x³?
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It is reflected in the x-axis; the S-curve goes from top-left to bottom-right instead of bottom-left to top-right.
What type of function is y = x³ − 4x?
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A cubic function (the highest power of x is 3).
What does solving 0 = 10 − x³ graphically involve?
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Finding where the graph of y = 10 − x³ crosses the x-axis (where y = 0).
Does the point (4, 64) lie on the graph of y = x³?
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Yes, because 4³ = 64.
What is the highest power of x in a cubic function?
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3 (the term x³ is the highest power).
In y = x³ + 2x² − 1, how many turning points can the graph have at most?
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Two turning points (a cubic can have 0, 1, or 2 turning points).
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