A+ » VCE » Maths Methods U3 & 4 Master Notes » A1 Functions and Graphs » Inverted Parabolic

Inverted Parabolic

1.7 Additional Graph Types


A picture containing chart Description automatically generated
  • The equation of a ‘standard’ circle is x^{2}+y^{2}=r^{2}.
    This circle has a radius of r, and its centre is the origin (0,\ 0).

E.g. The right shows the graph of the circle with equation x^{2}+y^{2}=4.

Note: Be careful here that the radius is 2, and not 4 as it should be r^{2}=4,\ r=2.

  • By definition r>0 as it signifies the radius of the circle. However, if we observe the equation, r can be negative too (the interpretation of the negative sign will involve a concept called ‘vectors’).
  • As we can see, x and y both have a range of [-r,\ r].
Read More »1.7 Additional Graph Types