Difference between revisions of "Optimization"
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It involves [[conversion|converting]] a quadratic to the [[standard form]] <math>a(x-h)^2+k</math> by [[completing the square]], then applying the [[Trivial Inequality]]. Then the maximum or minimum (it depends on which way the [[graph]] of the quadratic is facing) is <math>k</math>. | It involves [[conversion|converting]] a quadratic to the [[standard form]] <math>a(x-h)^2+k</math> by [[completing the square]], then applying the [[Trivial Inequality]]. Then the maximum or minimum (it depends on which way the [[graph]] of the quadratic is facing) is <math>k</math>. | ||
| − | ===Formula=== | + | ==="Formula"=== |
To optimize a quadratic, one might use the method described above, or one could use this other, smoother, method: | To optimize a quadratic, one might use the method described above, or one could use this other, smoother, method: | ||
| − | If <math>a>0</math>, then the quadratic <math>ax^2+bx+c=0</math>reaches its minimum when <math>x=-\frac{b}{2a}</math>, while when <math>a<0</math>, the quadratic reaches its ''maximum'' when <math>x=-\frac{b}{2a}</math>. | + | If <math>a>0</math>, then the quadratic <math>ax^2+bx+c=0</math> reaches its minimum when <math>x=-\frac{b}{2a}</math>, while when <math>a<0</math>, the quadratic reaches its ''maximum'' when <math>x=-\frac{b}{2a}</math>. |
Revision as of 11:14, 15 May 2014
The optimization of a quadratic equation is the process to find the maximum or minimum of said quadratic.
Process
It involves converting a quadratic to the standard form 
by completing the square, then applying the Trivial Inequality. Then the maximum or minimum (it depends on which way the graph of the quadratic is facing) is 
.
"Formula"
To optimize a quadratic, one might use the method described above, or one could use this other, smoother, method:
If 
, then the quadratic 
reaches its minimum when 
, while when 
, the quadratic reaches its maximum when .
