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Course: Algebra (all content) > Unit 9
Lesson 7: The quadratic formula- The quadratic formula
- Understanding the quadratic formula
- Using the quadratic formula
- Worked example: quadratic formula
- Worked example: quadratic formula (example 2)
- Worked example: quadratic formula (negative coefficients)
- Quadratic formula
- Using the quadratic formula: number of solutions
- Number of solutions of quadratic equations
- Proof of the quadratic formula
- Quadratic formula review
- Discriminant review
- Quadratic formula proof review
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Quadratic formula proof review
A text-based proof (not video) of the quadratic formula
The quadratic formula says that
for any quadratic equation like:
If you've never seen this formula proven before, you might like to watch a video proof, but if you're just reviewing or prefer a text-based proof, here it is:
The proof
We'll start with the general form of the equation and do a whole bunch of algebra to solve for . At the heart of the proof is the technique called . If you're unfamiliar with this technique, you may want to brush up by watching a video.
Part 1: Completing the square
Part 2: Algebra! Algebra! Algebra!
Remember, our goal is to solve for .
And we're done!
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