4.2-2 Constructing Polynomial
Functions
• Now, we have learned about several
properties for polynomial functions
– Finding y-intercepts
– Finding x-intercepts (zeros)
– End behavior (leading coefficient, degree)
– Testing values for zeros/factors (synthetic division)
• Knowing these properties, we can look to
construct a polynomial given particular
attributes
– Locations of x/y intercepts
– End behaviors (infinity, or negative infinity)
– Degrees (largest power)
– Specific coefficients
• Remember, the value k is a zero, if and only if,
x – k is a factor of p(x)
• After constructing a polynomial, we can use
our graphing calculators to help us verify
• Example. Construct a polynomial with the
following properties: Third degree, zeros of -3,
2, and 5, and as x -> ∞, f(x) -> - ∞
• Example. Construct a polynomial with the
following properties: fourth degree, zeros of 6, -4, 2, and a y-intercept of 18.
• Example. Construct a polynomial with the
following properties: zeros of 2, -3, and -4,
fifth degree, y-intercept of 48, and as x -> ∞,
f(x) -> - ∞
• Take our your graphing calculators. We can
now use them to help us confer/better put
together our solutions.
• Assignment
• Pg. 322
• 49-56, ALL