Unit Five: Lesson 2: Graphs of Polynomial Functions
Part Two: Even Degree Polynomials
Today we will look at functions with even degree.
y  x2
y  x 4 and so on.
For example, the family of functions
y  x6

For each of the following quartic functions, use the graphing calculator to sketch a neat graph.
a) y  x 4  2x 2  3
d) y   x 4  4 x 3  4 x 2  5
b) y  x 4  4 x 3  2x 2  12x
e) y  3x 4  28x 3  90x 2  108x  28

c)

of two of the graphs on one grid. Be sure to label them.
Use the grids below. Put a maximum
y  x 4  2x3  x 2  2x

f) y   x 4  7 x 3  11x 2  7 x  12
1
2




Using the graphs you just completed, state the x-intercepts and the end behaviour in the table below.
Function
a) y  x 4  2x 2  3
b) y  x 4  4 x 3  2x 2  12x
c) y  x 4  2 x 3  x 2  2 x
d) y   x 4  4 x 3  4 x 2  5
e) y  3x 4  28x 3  90x 2  108x  28
f) y   x 4  7 x 3  11x 2  7 x  12
x-intercepts
End Behaviour on the
right as x  

End Behaviour on the
left
as x  

Answer the following questions:
1. When the leading coefficient is negative, how does the graph change compared to when the leading
coefficient is positive?
________________________________________________________________________________________________________________________
2. When the leading coefficient is positive, the quartic graphs extend FROM quadrant number __________ to
quadrant number __________________.
3. When the leading coefficient is negative, the quartic graphs extend FROM quadrant number __________ to
quadrant number __________________.
3