Waste less time on Facebook — follow Brilliant.
×

1) Derivation of the quadratic formula

This is note \(1\) in a set of notes showing how to obtain formulas. There will be no words beyond these short paragraphs as the rest will either consist of images or algebra showing the steps needed to derive the formula mentioned in the title.

Suggestions for other formulas to derive are welcome, however whether they are completed or not depends on my ability to derive them. The suggestions given aren't guaranteed to be the next one in the set but they will be done eventually.


1 \[\large ax^2 + bx + c = 0\]


2 \[\large x^2 + \frac{b}{a}x + \frac{c}{a} = 0\]


3.1 \[\large x^2 + \frac{b}{a}x = \left(x + \frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2\]


3.2 \[\large \left(x + \frac{b}{2a}\right)^2 - \left(\frac{b}{2a}\right)^2 + \frac{c}{a} = 0\]


4 \[\large \left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a^2} + \frac{4ac}{4a^2} = 0\]


5 \[\large \left(x + \frac{b}{2a}\right)^2 = \frac{b^2 - 4ac}{4a^2}\]


6 \[\large x + \frac{b}{2a} = \pm\sqrt{\frac{b^2 - 4ac}{4a^2}}\]


7 \[\large x + \frac{b}{2a} = \frac{\pm\sqrt{b^2 - 4ac}}{2a}\]


8 \[\large x = \frac{- b \pm\sqrt{b^2 - 4ac}}{2a}\]

Note by Jack Rawlin
1 year, 10 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Yup! This is the derivation of the quadratic formula. Great!

Pi Han Goh - 1 year, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...