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Algebra 1 · Chapter 11 · Lesson 11.8 · Printable PDF

Deriving the Quadratic Formula Worksheet with Answer Key

6 problems on deriving the quadratic formula: the center and distance parts, sum and product checks, finding a mistake in a derivation, chairs in rows, special cases when a coefficient is 0, and another derivation by substitution. 2 pages, with a worked answer key.

6 problems2 pagesanswer key
Printable Deriving the quadratic formula worksheet with answer key - Algebra 1 (Page 1 PDF preview)
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What's on the worksheet

  1. For each equation, find the center and the distance from the center to each solution.
    x^2 - 8x + 11 = 02x^2 + 6x - 1 = 04x^2 - 12x + 7 = 0-x^2 + 4x + 1 = 03x^2 + 2x - 4 = 0
  2. Use the sum and product of solutions to check which pair is correct, without using the formula.
  3. Find the mistake in Priya's derivation of the quadratic formula.
  4. School concert chairs: set up a quadratic for rows and chairs and solve it.
  5. Show that the formula agrees with shorter methods when one coefficient is 0.
  6. Derive the formula another way by shifting the unknown.

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

Deriving the quadratic formula: the lesson ›

More Chapter 11 worksheets: Solving quadratic equations