# Precalculus 2.1-2.4 Test Outline

From Huben's Wiki

Quadratic Functions

- domain, range, intercepts, decreasing and increasing intervals, axis of symmetry, vertex, direction of opening
- transformations
- standard form: f(x) = a(x - h)
^{2}+ k- write equations from vertex and point

- quadratic formula

Polynomial Functions

- Standard form for degree n: f(x) = a
_{n}x^{n}+ ... + a_{0} - Include constant, linear, quadratic, cubic, quartic.
- domain, continuity
- leading coefficient test (end behavior)
- zero, root, solution, x-intercept, factor
- multiplicity: repeated zeros, whether crosses x-axis (odd) or not (even)
- making a polynomial function with given zeros
- intermediate value theorem

Real Zeros of Polynomials

- the division algorithm
- long division (can divide by anything)
- synthetic division (can only divide by (x - k))
- remainder theorem
- factor theorem
- rational zeros
- finding all zeros
- divide by each factor as you find it to simplify problem
- any common factors of x?
- use your calculator to see which rational zeros look good
- when the problem is simplified to a quadratic, use the quadratic formula

Complex numbers

- standard form, a + bi
- equality, conjugates, powers of i
- add, subtract, multiply, divide
- complex solutions to quadratic equations