Algebra II

Advanced algebraic concepts including polynomials, rational expressions, and complex numbers.

Polynomials and Their PropertiesFactoring and Solving Polynomial EquationsRational Expressions and Equations
Complex Numbers and Imaginary UnitsPolynomial Functions and Their GraphsSolving Systems of Equations Algebraically
Modeling Real-World Data with PolynomialsEngineering and Physics ApplicationsFinance and Business Mathematics
Mastering Factoring TechniquesEfficient Equation Solving
Polynomials and Thei...Factoring and Solvin...Rational Expressions...Complex Numbers and ...Polynomial Functions...Solving Systems of E...Modeling Real-World ...Engineering and Phys...Finance and Business...Mastering Factoring ...Efficient Equation S...
Advanced Topics

Polynomial Functions and Their Graphs

Seeing Polynomials in Action

Polynomial functions create some of the most interesting and wavy curves on a graph! The degree and the coefficients affect how the graph looks.

Key Features

  • End Behavior: How the graph acts for very large or small values of x.
  • Turning Points: Places where the graph changes direction.
  • Zeros/Roots: Where the graph crosses the x-axis.

Sketching Graphs

Find the zeros, plot a few points, and look at the degree and leading coefficient to predict the graph's shape.

Real-World Graphs

Polynomial graphs can model roller coasters, population changes, or even the path of a basketball.

Why Graphs Matter

Graphs turn numbers into pictures, helping us see trends and make predictions!

Examples

  • The graph of \( y = x^2 \) is a parabola opening upwards.

  • A cubic like \( y = x^3 - 2x \) crosses the x-axis three times.

In a Nutshell

The graph of a polynomial function shows its zeros, turning points, and how it behaves as x gets very big or very small.

Next
Solving Systems of Equations Algebraically