Quartics Investigation
1. Sketch the following graphs with the help of your graphics calculator. Use a
separate set of axes for each.
a) y  x 4
b) y  3x 4
c) y  2 x 4
d) y  ( x  1)4  3
e) y  2( x  1)4  2
2. Use your knowledge from 1. to explain the shape of graphs in the form
y  a ( x  h) 4  k
3. Sketch the following graphs with the help of your graphics calculator. Use a
separate set of axes for each.
a) y  x( x  1)( x  2)( x  3)
b) y  2 x( x  1)( x  2)( x  3)
c) y  ( x  5)( x  3)( x  2)( x  1)
4. Comment on the nature of the graphs found in the form
y  a( x  b)( x  c)( x  d )( x  e)
5. Investigate further to find a general rule for a quartic graph with 2 turning
points on the x-axis.
6. Sketch two different quartic graphs with a point of inflexion on the x-axis.
How many other x-intercepts are possible? Write a general rule for this type
of function.
7. Sketch a quartic graph with one x-intercept only. Find a general rule for a
function of this type.
Challenge:
1. How many different quartic graph shapes are possible?
2. Sketch a graph with a point of inflexion on the x-axis, a turning point on the xaxis, and one other x-intercept. Write a rule for this function.