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Quadratic Equations 4077 Views


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Description:

Quadratic equations can turn any frown upside down.

Language:
English Language

Transcript

00:04

Quadratic equations, a la Shmoop. Ever since ancient Greece, the word "quad"

00:09

has always meant "4." Quadrupeds walk on 4 legs...[roman man in forum]

00:13

...quadrilaterals have 4 sides...

00:16

...and a quadrillion comes after a trillion.

00:18

It'd be a nice number to have in your bank account.

00:21

But... where's the 4 in a quadratic equation? Quadratic equations are algebraic equations

00:26

where the highest exponent of x is 2. Maybe a quadratic equation always has to have

00:32

4 terms, but... ...nope. Not always the case, since this is

00:37

also a quadratic equation. But what about the graphs of quadratic equations?

00:41

What do they have to say for themselves? A graph of a quadratic equation forms something

00:49

called a parabola...

00:50

...which is really just a curve that looks like a smile...[smiling graph]

00:53

... or a frown...

00:54

...Parabolas have mood swings, too. The different moods that parabolas can have

01:00

depend on their quadratic equation. More specifically, it can depend on the coefficients

01:05

that x has in the quadratic equation. We named these three coefficients a, b, and

01:10

c, but you can call them whatever you want.

01:13

Alvin, Simon, and Theodore seem to be pretty popular choices. [chipmunks appear in formula]

01:16

Just like in real life, a smile is positive and a frown is negative... "a," that is.

01:21

The larger "a" is in magnitude, the narrower the smile...

01:25

...the smaller "a" is, the wider the smile. You could also give it some chocolate.

01:28

Always works for us, anyway. But even a, b, and c are only three coefficients,

01:32

not four.

01:33

Where is the four?! Even if we move the parabola up or down, it'll

01:38

still only cross the x-axis once... ...twice...

01:42

...or not at all... Even ways of solving quadratic equations are

01:46

3 and not 4.

01:48

To solve for x, we can... ...Factor...

01:51

...Complete the square... ...Or use the quadratic formula.

01:55

So after all that, why are they called quadratic equations? Where's the 4?

02:01

Ready? Drum roll, please... "Quadratus" is Latin for "square."

02:09

Talk about anti-climactic. [chimp scratching it's head]

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