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Precalculus » B. Quadratic, Polynomial, and Exponential Functions

  • B.1. Quadratic Functions

    1. B.1.M. Play Multiplayer 0 wins, 0 losses

    2. B.1.Q. Unit Challenge

    3. B.1.1. Writing equations of quadratics

      1. B.1.1.O. Overview
      2. B.1.1.1. Writing equations of parabolas given a graph
      3. B.1.1.2. Writing equations of parabolas given a vertex and point
      4. B.1.1.3. Writing quadratic equations given x-intercepts

    4. B.1.2. Vertex, axis of symmetry, and x-intercepts of quadratics

      1. B.1.2.1. Finding the vertex, axis of symmetry, and x-intercepts
      2. B.1.2.2. Word problems – Finding minimums and maximums
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  • B.2. Polynomial Functions

    1. B.2.M. Play Multiplayer 0 wins, 0 losses

    2. B.2.Q. Unit Challenge

    3. B.2.1. End Behavior and Zeros of Polynomials

      1. B.2.1.O. Overview
      2. B.2.1.1. Describe the right-hand and left-hand end behavior of the function
      3. B.2.1.2. Finding the real zeros of a polynomial function
      4. B.2.1.3. Determine the multiplicity of each zero and the number of turning points of the graph of the function
      5. B.2.1.4. Approximate a zero of a polynomial function
      6. B.2.1.5. Write a polynomial function with the given zeros
      7. B.2.1.6. Write a polynomial function with the given zeros and degree

    4. B.2.2. Polynomials and Synthetic Division

      1. B.2.2.O. Overview
      2. B.2.2.1. Polynomial Long Division
      3. B.2.2.2. Synthetic Division
      4. B.2.2.3. Write the function in the form f(x)=(x-k)q(x)+r for the given value of k
      5. B.2.2.4. Use the remainder theorem and synthetic division to find the value of the function
      6. B.2.2.5. Factor the polynomial completely using synthetic division given one solution
      7. B.2.2.6. Verify the given factors of the function and find the remaining factors of the function
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  • B.3. Complex Numbers

    1. B.3.M. Play Multiplayer 0 wins, 0 losses

    2. B.3.Q. Unit Challenge

    3. B.3.1. Operations

      1. B.3.1.O. Overview
      2. B.3.1.1. Adding and Subtracting Complex Numbers
      3. B.3.1.2. Multiplying Complex Numbers

    4. B.3.2. Complex Conjugates

      1. B.3.2.O. Overview
      2. B.3.2.1. Multiplying Complex Conjugates
      3. B.3.2.2. Writing a Quotient of Complex Numbers in Standard Form

    5. B.3.3. Writing Complex Numbers in Standard Form

      1. B.3.3.O. Overview
      2. B.3.3.1. Basic
      3. B.3.3.2. Multiplying or squaring imaginary numbers
      4. B.3.3.3. Simplify the complex number and write in standard form

    6. B.3.4. Complex Solutions of a Quadratic Equation

      1. B.3.4.O. Overview
      2. B.3.4.1. Use the quadratic formula to solve the quadratic equation
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  • B.4. Zeros and Polynomial Functions

    1. B.4.M. Play Multiplayer 0 wins, 0 losses

    2. B.4.Q. Unit Challenge

    3. B.4.1. Rational and Real Zeros

      1. B.4.1.O. Overview
      2. B.4.1.1. Find all zeros of the function given an equation
      3. B.4.1.2. Use the rational zero test to list the possible rational zeros of the function
      4. B.4.1.3. Find all rational zeros of the function
      5. B.4.1.4. Find all real solutions of the polynomial equation

    4. B.4.2. Imaginary Solutions and Conjugate Pairs

      1. B.4.2.O. Overview
      2. B.4.2.1. Find a polynomial function with real coefficients that has the given zeros
      3. B.4.2.2. Use the given zero to find all zeros of the function
      4. B.4.2.3. Find all zeros of the function and write the polynomial as a product of linear factors
      5. B.4.2.4. Use Descartes’s Rule of Signs to determine the possible numbers of positive and negative zeros of the function
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  • B.5. Rational Functions

    1. B.5.M. Play Multiplayer 0 wins, 0 losses

    2. B.5.Q. Unit Challenge

    3. B.5.1. Domain, vertical asymptotes, and horizontal asymptotes

      1. B.5.1.O. Overview
      2. B.5.1.1. Finding the domain of a rational function
      3. B.5.1.2. Finding vertical and horizontal asymptotes

    4. B.5.2. Graphs of rational functions

      1. B.5.2.O. Overview
      2. B.5.2.1. Sketching the graph of a rational function when the numerator is a larger degree
      3. B.5.2.2. Sketching the graph of a rational function when the numerator and denominator are the same degree
      4. B.5.2.3. Sketching the graph of a rational function when the denominator is a larger degree
      5. B.5.2.4. Sketching a rational function with common factors
      6. B.5.2.5. Rational Functions with Slant Asymptotes
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  • B.6. Polynomial and Rational Inequalities

    1. B.6.M. Play Multiplayer 0 wins, 0 losses

    2. B.6.Q. Unit Challenge

    3. B.6.1. Solving Inequalities

      1. B.6.1.O. Overview
      2. B.6.1.1. Determine whether the x-value is a solution of the inequality
      3. B.6.1.2. Solving a polynomial inequality
      4. B.6.1.3. Solving a rational inequality
      5. B.6.1.4. Word Problems – Cost, Revenue, and Profit
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