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Year 10 / GCSE · Maths

Graphs And Coordinates

Year 10 / GCSE learners practise graph transformations and quadratic graphs gcse.

The activities include Apply Horizontal Translations to a Graph Using y = f(x + a), Interpret the Gradient and Intercept of a Straight Line, Apply Transformations to a Graph Using y = af(x), and related practice. The checked support below includes video, worksheet, teaching, practice. Open a resource in its provider's website and choose the format that best helps the learner explain the idea independently.

Activities covered

  • Apply Horizontal Translations to a Graph Using y = f(x + a)
  • Interpret the Gradient and Intercept of a Straight Line
  • Apply Transformations to a Graph Using y = af(x)
  • Apply Transformations to a Graph Using y = -f(x) and y = f(-x)
  • Apply Transformations to a Graph Using y = f(ax)
  • Apply Vertical Translations to Graphs Using y = f(x) ± a
  • Find Approximate Solutions to Quadratics Using a Graph
  • Find the Equation of a Straight Line
  • Interpret Distance-Time Graphs
  • Interpret Speed-Time Graphs
  • Use Algebra to Identify the Roots of a Quadratic
  • Use Algebra to Identify the Turning Point of a Quadratic
  • Use the Equation for a Circle
  • Use the Equation of a Tangent to a Circle

Checked learning resources

  • Horizontal graph translations: y = f(x + a)

    Oak National Academy · Video · Opens on the provider website

    GCSE Higher lesson applies y = f(x + a), translating every point horizontally by a units in the opposite direction while preserving the graph shape.

  • y = mx + c

    Corbett Maths · Video · Opens on the provider website

    GCSE video identifies m as the gradient or rate of change and c as the y-intercept or starting value, then writes and interprets straight-line equations.

  • Vertical stretches: y = af(x)

    Oak National Academy · Video · Opens on the provider website

    GCSE Higher lesson applies y = af(x), multiplying every y-coordinate by a to produce a stretch with scale factor a in the y-direction.

  • Transformations of graphs

    Corbett Maths · Video · Opens on the provider website

    GCSE Higher video distinguishes vertical and horizontal translations, stretches and the reflections y = -f(x) and y = f(-x) from their function notation.

  • Horizontal stretches: y = f(ax)

    Oak National Academy · Video · Opens on the provider website

    GCSE Higher lesson applies y = f(ax), multiplying inputs before evaluation and producing a horizontal stretch with scale factor 1/a in the x-direction.

  • Vertical graph translations: y = f(x) + a

    Oak National Academy · Video · Opens on the provider website

    GCSE Higher lesson applies y = f(x) + a, translating every point vertically by a units while leaving all x-coordinates unchanged.

  • Solving quadratics graphically

    Corbett Maths · Video · Opens on the provider website

    GCSE video estimates quadratic roots from x-axis intersections and solves related equations by reading the appropriate horizontal level on a supplied quadratic graph.

  • Equation of a line through two points

    Corbett Maths · Video · Opens on the provider website

    GCSE video calculates gradient from two coordinate pairs, substitutes a point into y = mx + c and finds the full straight-line equation.