Zeros and end behavior

Math

Definition

Zeros of a function are the x-values where the function equals zero (where the graph crosses or touches the x-axis). End behavior describes what happens to the y-values as x approaches positive or negative infinity, determined by the leading term of a polynomial.

Examples

  • The zeros of f(x) = x² − 4 are x = 2 and x = −2
  • For f(x) = x³, end behavior is: as x → ∞, f(x) → ∞ and as x → −∞, f(x) → −∞
  • An even-degree polynomial with positive leading coefficient rises on both ends
Key Fact

Even degree + positive lead: both ends up; Odd degree + positive lead: left down, right up

Related Terms

Zeros and multiplicity End behavior X and y intercepts Solving by factoring

Study This Concept

Practice zeros and end behavior with free review games in these units:

Algebra 2 Unit 4: Polynomial Functions