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Welcome to GCSE Edexcel Maths revision.

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Topic M 13: Quadratic and other graphs.

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This video covers Higher tier.

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It includes the shared content and the labelled Higher extensions.

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The graph of y equals x squared is a U-shaped parabola with minimum open bracket 0, 0 close bracket , symmetric about the y-axis. y equals minus x squared opens downward.

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Generate values from the equation rather than guessing the curve.

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Graph of y equals x squared minus four

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For y equals x squared minus 4, the y-intercept is minus 4 and the roots are x equals minus 2 and x equals 2.

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Roots are where y equals 0, not where x equals 0.

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The turning point is the minimum or maximum.

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A quadratic's symmetry line passes through it; use symmetry to help read missing points.

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The graph of y equals x cubed passes through the origin and increases from bottom left to top right.

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Its values are negative when x is negative.

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The graph of y equals the fraction with numerator open bracket 1 close bracket and denominator open bracket x close bracket ,

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end fraction has two branches and is undefined at x equals 0.

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The axes are asymptotes: the graph approaches them but never meets them.

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Graph of y equals one over x

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Find roots from a factorisation when possible. y equals open bracket x minus 1 close bracket multiplied by open bracket x plus 3 close bracket has roots 1 and minus 3,

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so its symmetry line is halfway between them,

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x equals minus 1.

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Read an intersection's coordinates using the graph scale.

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State approximate values when the graph does not show an exact solution.

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Write y equals x squared plus 6 x plus 5 as y equals open bracket x plus 3 close bracket squared minus 4.

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Its turning point is open bracket minus 3, minus 4 close bracket , because the squared term's smallest value is 0.

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For y equals 2 to the power of open bracket x close bracket , values double when x increases by 1.

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It passes through open bracket 0, 1 close bracket , remains positive and approaches y equals 0 as x becomes very negative.

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Exponential growth is not constant addition.

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Graph of y equals two to the power x

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For y equals k to the power of open bracket x close bracket with 0 is less than k is less than 1, the graph shows exponential decay.

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For example, y equals open bracket 1 over 2 close bracket to the power of open bracket x close bracket halves for each step to the right.

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Angles are in degrees at GCSE. y equals sine x has period 360 degrees,

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range minus 1 to 1,

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and zeros at multiples of 180 degrees. y equals cosine x has the same period and range but starts at 1 when x equals 0 degrees.

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Sine and cosine over one full turn

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y equals tangent x has period 180 degrees, zeros at multiples of 180 degrees, and vertical asymptotes at 90 degrees plus 180 degreesn.

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It is undefined at those angles; do not join a curve across an asymptote.

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Tangent graph and its asymptotes

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Use graph symmetry and periodicity to find more than one solution in a stated interval. sine x equals 0.5 gives x equals 30 degrees and 150 degrees for 0 degrees is less than or equal to x is less than or equal to 360 degrees.

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That completes Quadratic and other graphs.

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Revisit the notes and test yourself on the revision website.