AQA · Mathematics · 8300
GCSE Maths: Quadratic graph (completing the square)
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths video for Quadratic graph (completing the square) (Corbettmaths Video 371), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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Where does the graph y = f(x + a) sit relative to y = f(x)?
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Translated a units to the left (counterintuitively, adding inside the bracket shifts left).
Where does the graph y = f(x − a) sit relative to y = f(x)?
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Translated a units to the right.
The graph y = f(x) + a is the graph y = f(x) translated a units ?.
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upwards
What is the turning point of y = (x + a)² + b?
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(−a, b): the graph of y = x² is shifted a to the left and b up.
Write x² + 4x + 7 in the form (x + a)² + b.
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(x + 2)² + 3, since (x + 2)² − 4 + 7 = (x + 2)² + 3.
What is the turning point of y = x² + 4x + 7?
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(−2, 3). Completing the square gives (x + 2)² + 3.
How do you find where a quadratic graph crosses the y-axis?
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Substitute x = 0 into the equation; the y-intercept is the constant term.
Write x² − 8x + 1 in the form (x + a)² + b.
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(x − 4)² − 15, since (x − 4)² − 16 + 1 = (x − 4)² − 15.
What is the turning point of y = x² − 8x + 1?
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(4, −15). Completing the square gives (x − 4)² − 15.
The graph y = x² + ax + b has turning point (5, 1). Find a and b.
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a = −10, b = 26. Expand (x − 5)² + 1 = x² − 10x + 26.
Which A-level topic offers an alternative method for finding turning points of quadratics?
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Calculus (differentiation).
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