## Other Graphs 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 If c is positive. e.g. xy = 4 If c is negative. e.g. xy = - 4  Graph is in first and third quadrants. Graph is in second and fourth quadrants.

### 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 = 3 ### Cubics

The general equation of a cubic function is y = (x − a)(x − b)(x − c)

The simplest cubic is y = x3.

e.g.

 y = x3 y = (x − 1)(x − 3)(x + 2)  ### Summary of Graphs

 Type of graph General equation Characteristics Example Straight line ax + by + c = 0 y = mx + c x and y terms both have exponents of 1 x + 2y = 6 y = 3x + 4 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 Hyperbola xy = c x and y terms have exponents of 1 xy = 6 Circle x 2 + y 2 = a2 x and y terms both have exponents of 2 x 2 + y 2 = 16 Growth curve(exponential) y = a x x is the exponent y = 5x Cubic y = (x − a)(x − b)(x − c) x term has exponent of 3 y = (x − a)(x − b)(x − c)