MHF 4U1 Advanced Functions
Polynomial Functions Polynomials in Factored Form
Consider the following functions:
f ( x) = x 2 + 5 x + 6
g ( x) = 2 x 2 + 10 x + 12
Now consider…
f ( x) = ( x − 2) 2 ( x + 3) f ( x) = ( x − 2) 3 ( x + 3)
Summarize:
Polynomial Order Behaviour Near the Root
y = (x - 2)(x + 3)
y = (x - 2)2(x + 3)
y = (x - 2)3(x + 3)
Let’s Practice
eg1. Sketch a possible graph of the following functions.
a) f ( x) = x( x − 4)( x − 1) b) f ( x) = ( x + 1) 3
c) f ( x) = ( x + 2)( x − 1)( x − 3) 2 d) f ( x) = x 4 + 2 x 3
2
eg2. Determine the equation of a cubic function that has zeros at -2, 3, and . The function also
5
has a y-intercept of 6.
eg3. Determine the equation of the following function.
eg4. While playing in the surf, a dolphin jumped twice in the air before diving deep below the
surface of the water. The path of the dolphin is shown on the following graph. Write the
equation of the polynomial function that represents the height of the dolphin relative to the
surface of the water.