EVALUATING POLYNOMIAL FUNCTIONS
A polynomial function can be evaluated GRAPHICALLY by using the graph of the function to
determine the y-value for the given x-value.
y

x








Consider the polynomial function y = x3 -2x2 – 3x ,
graphed at left.


Determine the value for y, when x = 1.




A polynomial function can be evaluated NUMERICALLY by substituting the given x-value into
the polynomial expression and then performing the required operations to determine the
y-value. On the graphing calculator, this can be found using the TABLE function.
Consider the polynomial function f(x) = x3 - 2x2 – 3x. Determine: a) f(4) b) f(-3) c) f(x + 1).
A polynomial function can model a real-world situation, such as the VOLUME of a prism.
The dimensions of a rectangular packing box are shown on the diagram below. The volume
of the box can be modelled by the polynomial function, V(x) = x(45 – 2x)(28 – 2x).
Determine the volume of the box when x = 10 cm.
EVALUATING POLYNOMIAL FUNCTIONS WORKSHEET
1. Consider the polynomial function f(x) = 2x3 + 7x2 + 3x – 4. Evaluate the polynomial function for each of
the following values.
a) x = 4
b) x = -3
c) x = 0
d) x = -2
What is the y-intercept of this polynomial function? _____ Do you need to calculate it, to determine
it? Why or why not? ________________________________________
2. Consider the polynomial function f(x) = 3x4 + 2x3 – x2 + 2x – 3. Evaluate the polynomial function for
each of the following values.
a) x = 3
b) x = -5
c) x = -4
d) x = 2
Without calculating it, what is the y-intercept of this polynomial function? _____
3. Evaluate each of the following functions for the indicated x-value.
a) f(x) = 3x2 + 2, f(-1)
b) g(x) = -2x3 + 4x, g(3)
c) h(x) = x4 – 3x2, h(2)
d) f(x) = 2x5 – 5x2, f(-2)
e) g(x) = -2x4 + 3x3 – 4x2 + 5x -1, g(4)
f) h(x) = -1/4x3 + x2 – 2x + 3, h(-2)
4. Consider the polynomial function f(x) = x2 + 2x.
a) Determine an expression for f(a).
b) Determine an expression in simplified form for f(x + 2).
c) Determine an expression in simplified form for f(x – 3).
d) Determine an expression in simplified form for f(x2 + 2x)
5. David designs a rectangular storage box with dimensions of: (x) cm, (25 – 2x) cm, and
a) Determine a polynomial function which models the volume of David’s storage box.
b) Determine the volume of David’s box if x = 8cm.
c) Can David’s box exist, if x = 15 cm? Why or why not?
(35 – 2x) cm.
6. a) Determine a function that models the volume of a cylinder whose height is double its radius.
b) Determine the volume of the cylinder in (a), when the radius is 5 cm.
7. The length of a rectangular dog run is 3 m more than twice the width.
a) Show this information on a diagram.
b) Determine a function that expresses the area of the dog run in terms of its width.
c) Determine the area when the width is 4 m.
d) What width would produce an area of 50 m2? {Oh, no, I have to remember how to solve for the
roots of a quadratic equation!}