A-Level Maths | Graphs & Transformations

Straight-line graphs

The equation of a straight line is always in the form y=mx+c

m: the gradient

c: the y-intercept

To sketch a straight-line graph, draw a line through the y-intercept and the x-intercept.

Circles

The equation of a circle is always in the form (x-a)²+(y-b)² = r²

Centre: (a, b)

Radius: of the circle is r

You can find four of the points on the circle by using (a+r, b), (a-r, b) (a, b+r) and (a, b-r)

Quadratics

The equation of a quadratic is always in the form y = ax² + bx + c

A quadratic is always U-shaped

The equation of a quadratic can be written in the form y = k(x-a)(x-b) where (a, 0) and (b, 0) are the x-intercepts.

The equation of a quadratic can also be written in the form y = k(x-a)² + b where (a, b) is the turning point.

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Cubics

The equation of a cubic can be written in the form y= ax³+bx²+cx+d.

A cubic graph is N-shaped.

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Quartics

The equation of a quartic is always in the form y = ax⁴+bx³+cx²+dx+e

A quartic graph is always W-shaped

Reciprocal graphs

A reciprocal graph is written in the form y = k/x or y = k/x²

These graphs have asymptotes at y=0 and x=0.

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