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Algebra 2 · Chapter 3 · Lesson 3.2 · Printable PDF

Cubic, Quartic and Higher Degree Functions Worksheet with Answer Key

6 problems on cubic, quartic and higher degree functions: using b squared minus 3ac to predict turns, sign charts for polynomial inequalities, chords and bending, a cubic's inflection point and zeros, and a parcel box volume problem. 2 pages, with a worked answer key.

6 problems2 pagesanswer key
Printable Cubic, quartic and higher degree functions worksheet with answer key - Algebra 2 (Page 1 PDF preview)
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What's on the worksheet

  1. For each cubic, name the shape (no turn, flat point or two turns) and locate the turns.
    f(x) = x^3 - 3x^2 + 5xf(x) = x^3 + 6x^2 + 12x + 3f(x) = -x^3 + 6x^2 + 15x - 4f(x) = -8x^3 + 12x^2 - 6x + 1
  2. Solve each inequality with a sign chart, in interval notation.
    -x(x + 4)(x - 3) \ge 0x^3 - 4x^2 - 12x \le 0
  3. Find a chord's midpoint on a cubic and decide whether the graph bends up or down there.
  4. Find the third zero of a cubic from two zeros and its point of inflection.
  5. Find a cubic's valley from its inflection point and peak, then find a value.
  6. Word problem: the largest box that meets a parcel service's length-plus-girth limit.

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The free lesson teaches it with worked examples and practice problems.

Cubic, quartic and higher degree functions: the lesson ›

More Chapter 3 worksheets: Polynomial functions