# 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