Quadratic equations, a la Shmoop.
Ever since ancient Greece, the word "quad"
has always meant "4."
Quadrupeds walk on 4 legs...
...quadrilaterals have 4 sides...
...and a quadrillion comes after a trillion.
It'd be a nice number to have in your bank
account.
But... where's the 4 in a quadratic equation?
Quadratic equations are algebraic equations
where the highest exponent of x is 2.
Maybe a quadratic equation always has to have
4 terms, but...
...nope.
Not always the case, since this is also a
quadratic equation.
But what about the graphs of quadratic equations?
What do they have to say for themselves?
A graph of a quadratic equation forms something
called a parabola...
...which is really just a curve that looks
like a smile...
... or a frown...
...Parabolas have mood swings, too.
The different moods that parabolas can have
depend on their quadratic equation.
More specifically, it can depend on the coefficients
that x has in the quadratic equation.
We named these three coefficients a, b, and
c, but you can call them whatever you want.
Alvin, Simon, and Theodore seem to be pretty
popular choices.
Just like in real life, a smile is positive
and a frown is negative... "a," that is.
The larger "a" is in magnitude, the narrower
the smile...
...the smaller "a" is, the wider the smile.
You could also give it some chocolate.
Always works for us, anyway.
But even a, b, and c are only three coefficients,
not four.
Where is the four?!
Even if we move the parabola up or down, it'll
still only cross the x-axis once...
...twice...
...or not at all...
Even ways of solving quadratic equations are
3 and not 4.
To solve for x, we can...
...Factor...
...Complete the square...
...Or use the quadratic formula.
So after all that, why are they called quadratic
equations?
Where's the 4?
Ready?
Drum roll, please...
"Quadratus" is Latin for "square."
Talk about anti-climactic.
