Goal: Transform x^2 + a*x + b to (x + c)^2 + d.
Setting the two sides equal to each other:
x^2 + a*x + b = (x + c)^2 + d
x^2 + a*x + b = x^2 + 2*c*x + c^2 + d
Next I will use a technique that calculus students normally use when decomposing partial fractions.
Setting the coefficients of x^2, x, and the constant equal to each other, we have:
x^2: 1 = 1
x: a = 2*c
constant: b = c^2 + d
Solving for c:
a = 2*c
c = a/2
Then solving for d:
b = c^2 + d
b = a^2/4 + d
d = b  a^2/4
Hence:
x^2 + a*x + b = (x + a/2)^2 + (b  a^2/4)
Hope this helps. Until next time!
Eddie
This blog is property of Edward Shore. 2013
A blog is that is all about mathematics and calculators, two of my passions in life.
Monday, August 12, 2013
Completing the Square
Subscribe to:
Post Comments (Atom)
How to Rotate Graphs
How to Rotate Graphs Introduction The key is to use parametric equations in our rotation. Using the rotation angle θ, the rotatio...

Casio fx991EX Classwiz Review Casio FX991EX The next incarnation of the fx991 line of Casio calculators is the fx991 EX. ...

TI36X Pro Review This is a review of the TI36X Pro Calculator by Texas Instruments. History Originally, this was the TI30X Pro that w...

One of the missing features of the TI82/83/84 family is the ability to convert between bases. Here are two programs in TIBasic to help...
No comments:
Post a Comment