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Being able to sketch curves from their equations is an essential skill at A-Level. This lesson brings together the techniques needed to sketch polynomial, rational, parametric and other curves, as required by the Edexcel 9MA0 specification.
When asked to sketch a curve, systematically consider:
Set x = 0 and find y.
Set y = 0 and solve for x. Use factorisation, the quadratic formula, or the Factor Theorem as appropriate.
Example: y = x³ − 4x = x(x² − 4) = x(x − 2)(x + 2).
x-intercepts: x = 0, x = 2, x = −2. y-intercept: y = 0.
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