AQA · Mathematics · 8300
GCSE Maths: Quadratics: solving graphically
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Quadratics: solving graphically (Corbettmaths Video 267), 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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The solutions to a quadratic equation are also called the ? of the equation.
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roots
What does the turning point of a quadratic graph represent?
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The maximum or minimum point of the parabola, where the graph changes direction.
To solve x² − x − 5 = 0 graphically, what graph should you draw and what should you look for?
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Draw the graph of y = x² − x − 5 and find where it crosses the x-axis (where y = 0).
If you need to solve x² + 2x − 1 = 2 using a graph of y = x² + 2x − 1, what points should you find?
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Find where the graph y = x² + 2x − 1 intersects the horizontal line y = 2. The x-coordinates are the solutions.
If the graph of 2x² − 4x + 1 = k has exactly one solution, what does this tell you about k?
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k equals the y-coordinate of the turning point (vertex) of the parabola y = 2x² − 4x + 1.
How many solutions does a quadratic equation have if its graph touches the x-axis at exactly one point?
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One solution (a repeated root). This occurs when the vertex of the parabola lies on the x-axis.
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