A swift introduction to Quadratic Functions and Equations
What with the rain pouring outside, I figured a nice comfy armchair
and a relaxing book might just do the trick. Ah! Here we are, a nice well-loved
story from Pythagoras and Euclid:
Quadratic Function:
AX2 + BX + C = 0
The quadratic function is basically a blend of a parabolic
function, and the standard form equation. You can kind of see the similarity if
you swap the 0 out for a Y:
Y = AX2 + BX + C
However, the quadratic function will automatically set Y to
0 for you, leaving you free to concentrate on solving for the X’s. Why do we
even want to solve for the X’s? A quadratic equation deals with values of X and
X2, and has a graph that looks like a giant letter U, or n,
depending on whether the graph is positive or negative. The graph only crosses
the Y axis once, but it crosses the X axis twice! As curious mathematicians, we
are curious exactly when it crosses the X axis, or when Y=0. This is why we
take the Y out and Swap in 0 right off the bat.
Luckily, an old bunny with a gray beard by the name of
Pythagoras E. Bunny, and his younger neighbor, Euclid Lopear Bunny, have made
some headway for us. Typically when solving for X in an equation containing X2,
we can either start factoring, use a table or graph, or try to solve it by
completing the square (spoiler, completing the square is long and tedious). Py
and Euclid decided to create a general solution for completing the square in
order to make it faster and easier for all bunny-kind. Their resulting solution
was:
![x = [ -b ± sqrt(b^2 - 4ac) ] / 2a](file:///C:\Users\BMABRY~1.WOO\AppData\Local\Temp\msohtmlclip1\01\clip_image001.gif){kind=small}
Granted, this looks messy, it but actually simplifies
everything into 1 step: plug in your numbers and solve! Given: 0=1x2
+ 5x + 6, we plug 1 in for A, 5 in for B, and 6 in for C:
X= -2 +- sqrt(52-4*1*6) all over 2*3, or (-2+-1)
/2. It’s the plus or minus that often confuses people. We actually solve the
equation twice (remember, we are looking for 2 solutions, the 2 places X
crosses the X axis).
+ (-2+1) /2 = -1/2
-. (-2-1) /2 = -3/2
X = -1/2 or -3/2
This isn't comprehensive, but it's meant to be a quick refresher / reminder about lop eared bunnys, I mean Quadratic Equations.
Enjoy!
2 comments:
Conclusion: Sheepdogs can't handle too much creative writing. It makes them math-crazy. *nods*
Ahh yes, erm, I remember that! Sor tof. But the cool One Note program (shameless plug) can help you write the quadratic equation without having to find the symbols! Kind of neat. Anywho, I liked your riddle, and very good job with a refresher course!
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