AQA · Mathematics · 8300
GCSE Maths: Quadratic graphs: finding turning point
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Quadratic graphs: finding turning point (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 is the general vertex form of a quadratic equation?
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y = (x − h)² + k, where (h, k) is the turning point.
For a quadratic in the form y = (x − 3)² + 4, what are the coordinates of the turning point?
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(3, 4). The turning point is (h, k) when the equation is y = (x − h)² + k.
What algebraic technique is used to find the turning point of a quadratic written in the form y = x² + bx + c?
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Completing the square. This converts the quadratic to vertex form y = (x − h)² + k, where (h, k) is the turning point.
If a quadratic has turning point (h, k), what is the equation of its line of symmetry?
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x = h. The line of symmetry is a vertical line passing through the turning point.
Given that x² − 10x + 3 ≡ (x − a)² − b, what information can you immediately read from the completed square form?
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The turning point is (a, −b). The values a and b directly give the coordinates of the vertex.
When sketching y = x² + 4x − 6, what two key features should always be shown?
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The turning point and the y-intercept. These are the minimum required features for a basic quadratic sketch.
If a parabola has equation y = (x + a)² + b and the turning point has x-coordinate −1, what is the value of a?
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a = 1. The form y = (x − h)² + k has turning point at x = h, so (x + 1)² means x − (−1), giving h = −1.
How can you find the y-coordinate of the turning point if you know the x-coordinate?
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Substitute the x-coordinate into the equation and evaluate. The turning point lies on the curve.
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