Algebra 2: Polynomials & Functions

Polynomial

Expression with variables and coefficients using only addition, subtraction, multiplication, and non-negative integer exponents

Degree of a Polynomial

The highest exponent of the variable in the polynomial

Quadratic Function

f(x) = ax² + bx + c; graph is a parabola

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a; solves ax² + bx + c = 0

Discriminant

b² - 4ac; determines number of real solutions (positive: 2, zero: 1, negative: 0)

Vertex of a Parabola

The highest or lowest point; x = -b/(2a)

Completing the Square

Rewriting ax² + bx + c in the form a(x - h)² + k

Synthetic Division

Shortcut method for dividing a polynomial by (x - c)

Remainder Theorem

When polynomial f(x) is divided by (x - c), the remainder equals f(c)

Factor Theorem

(x - c) is a factor of f(x) if and only if f(c) = 0