Precalculus 2.1-2.4 Test Outline

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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) = anxn + ... + a0
  • 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
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