Math Is Fun Forum

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Minimum of the quadratic polynomial

For wihch x
ax^2+bx+c , a>0 is minimum?

Let {is} means"must be"
i. ax^2+bx+c {is} min =>
ii. ax^2+bx {is} min
iii. a(x^2+(b/a)x) {is} min
iv. x^2+(b/a)x {is} min =>
v. x^2+2(b/2a)x+(b/2a)^2 {is} min
vi. (x+b/2a)^2 {is} min, but
vii. p^2>=0, p∈R =>
viii. (x+b/2a)=0
x=-b/2a

So when x=-b/2a ax^2+bx+c has a minimum.

If a<0 in iii we'll divide by -|a|, so x=-b/2a is maximum.

Last edited by krassi_holmz (2005-12-29 07:22:17)

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krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Minimum of the quadratic polynomial

Cool!

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IPBLE:  Increasing Performance By Lowering Expectations.