Please note that this topic is now assessed at NCEA, Level 2 (Year 12).
There are several other types of graphs. These include hyperbolas, circles, growth curves and cubics.
These are shown below.
Hyperbolas
The general equation of a hyperbola is xy = c or 
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If c is positive. e.g. xy = 4 |
If c is negative. e.g. xy = - 4 |
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Circles
The general equation of a circle is x 2 + y 2 = a 2. , where a is the radius of the circle.
This relation is not a function, because some of the x-values have two corresponding y-values.
e.g. x 2 + y 2 = 9
Exponential Functions or Growth Curves
The general equation is y = ax
The greater the value of a, the steeper is the curve.
All growth curves of this type pass through the point (0, 1)
e.g. y = 3x 
Cubics
The general equation of a cubic function is y = (x − a)(x − b)(x − c)
The simplest cubic is y = x3.
e.g.
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y = x3 |
y = (x − 1)(x − 3)(x + 2) |
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Summary of Graphs
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Straight line |
ax + by + c = 0 y = mx + c |
x and y terms both have exponents of 1 |
x + 2y = 6 y = 3x + 4 |
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Parabola |
y = ax 2 + bx + c y = a(x − h)2 + k |
y term has exponent of 1 x term has exponent of 2 |
y = x 2 + 4x + 3 y = 2(x − 3)2 + 4 |
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Hyperbola |
xy = c |
x and y terms have exponents of 1 |
xy = 6 |
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Circle |
x 2 + y 2 = a2 |
x and y terms both have exponents of 2 |
x 2 + y 2 = 16 |
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Growth curve |
y = a x |
x is the exponent |
y = 5x |
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Cubic |
y = (x − a)(x − b)(x − c) |
x term has exponent of 3 |
y = (x − a)(x − b)(x − c) |
