AQA · Mathematics · 8300

GCSE Maths: Quadratics: solving graphically advanced

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Quadratics: solving graphically advanced (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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  1. To solve x² - 2x + 4 = 2 graphically, what two graphs must you draw?

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    y = x² - 2x + 4 and y = 2. The solutions are where these graphs intersect.

  2. Where on a graph do you find the solutions when solving a quadratic equation graphically?

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    At the x-coordinates of the intersection points of the two graphs.

  3. If you have the graph of y = x² - x - 2 and need to solve x² - 2x - 1 = 0, why can't you directly use the given graph?

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    Because the quadratic expression in the equation (x² - 2x - 1) is different from the given graph (x² - x - 2).

  4. To solve x² - 2x - 1 = 0 using the graph of y = x² - x - 2, what straight line should you draw?

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    y = x - 1. Rearranging: x² - x - 2 = x - 1 becomes x² - 2x - 1 = 0 when you subtract x and add 1 to both sides.

  5. When solving x² - x - 2 = 0 graphically, how do you determine what to add or subtract from both sides to match your target equation?

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    Compare the coefficients: determine what must be added or subtracted to transform the given quadratic into the target quadratic.

  6. To solve 2x² - 4x - 3 = 0 using the graph y = 2x² - x - 2, what linear equation must you set equal to the given quadratic?

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    y = 3x + 1. This is because subtracting 3x and subtracting 1 from both sides of 2x² - x - 2 = 3x + 1 gives 2x² - 4x - 3 = 0.

  7. What is the first step in solving x² + 2x - 3 = x + 2 graphically when given the curve y = x² + 2x - 3?

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    Draw the straight line y = x + 2 on the same axes as the quadratic curve.

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