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Quadratic Equations 4081 Views
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Description:
Quadratic equations can turn any frown upside down.
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.
Full Transcript
- 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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