Deriving the Quadratic Formula

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Examples, solutions, and videos to help Algebra I students learn how to derive the quadratic formula by completing the square for a general quadratic equation in standard form, ax2 + bx + c = 0 , and use it to verify the solutions for equations from the previous lesson for which they have already factored or completed the square.

New York State Common Core Math Algebra I, Module 4, Lesson 14

Worksheets for Algebra 1

Lesson 14 Summary

The quadratic formula is derived by completing the square on the general form of a quadratic equation ax2 + bx + c = 0, where a ≠ 0. The formula can be used to solve any quadratic equation and is especially useful for those that are not easily solved by using any other method (i.e., by factoring or completing the square).

The following diagram shows how to derive the Quadratic Formula. Scroll down the page for more examples and solutions on how to use the quadratic formula to solve equations.
Derive Quadratic Formula

Lesson 14 Problem Set Sample Solutions

Use the quadratic formula to solve each equation.

  1. Solve for z. z2 - 3z - 8 = 0
  2. Solve for q. q2 -8 = 3q
  3. Solve for m. 1/3 m2 + 2m + 8 = 5

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