AQA · Mathematics · 8300
GCSE Maths: Quadratic graphs: line of symmetry
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Quadratic graphs: line of symmetry (Corbettmaths Video 265), 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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What shape is a quadratic graph called?
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A parabola.
What does the line of symmetry of a quadratic graph look like?
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A vertical line passing straight through the middle of the parabola.
The equation of a line of symmetry of a quadratic graph is always of the form ?.
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x equals a constant
How do you find where a quadratic graph crosses the x-axis?
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Set y = 0 and solve the resulting equation (usually by factorising).
If a quadratic crosses the x-axis at x = -6 and x = 4, what is the equation of its line of symmetry?
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x = -1. The midpoint is calculated as (-6 + 4)/2 = -2/2 = -1.
In the transformation y = f(x + a), how does the graph of y = f(x) move?
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The graph translates a units to the left.
In the transformation y = f(x) + a, how does the graph of y = f(x) move?
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The graph translates a units upwards.
What is x² + 4x + 25 in completed square form?
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(x + 2)² + 21.
If a quadratic is written as y = (x + 2)² + 21, what is the equation of its line of symmetry?
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x = -2. The transformation (x + 2) shifts the graph 2 units left, so the line of symmetry passes through x = -2.
What is x² - 6x - 27 in completed square form?
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(x - 3)² - 36.
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