Math Is Fun Forum

RickyOswaldIOW

Member

Registered: 2005-11-18

Posts: 212

Quadratic Equations

Happy Easter everyone!

I've just been revising some of my earlier a-level work and I'm a little confused with this:

"Let f(x) = x^2 + 6x + 7.

(a)  Put f(x) into completed square form.

(b)  Solve the equation f(x) = 4."

I do know how to do all of this but I can't for the life of me see where they are getting f(x) = 4 from?!

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Aloha Nui means Goodbye.

RickyOswaldIOW

Member

Registered: 2005-11-18

Posts: 212

Re: Quadratic Equations

Are they just saying that for the sake of the example that (x + 3)^2 - 2 = 4?  That's mighty confusing since the next 50 pages that often use factorising and completing the square assume that f(x) = 0.

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Aloha Nui means Goodbye.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Quadratic Equations

This is a traditional way to solve a quadratic equation.

Typically, you shift the original function into a form
f(x) = (x+a)²+b

It does no matter that the function equal to any given value, because the equation formed can be easily solved.

f(x)=c
(x+a)²=c-b

or

hence

Actually, given a equation of standard form, the explicit solution fomula is derived by this procedure
ax²+bx+c=0
a(x+b/2a)²=b²/4-c
......

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X'(y-Xβ)=0

dimples

Member

Registered: 2006-04-21

Posts: 1

Re: Quadratic Equations

how can i write a two paragraph essay on "Solving Quadratic Equations by the Quadratic Formula"

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Quadratic Equations

Start here: Quadratic Equation Solver

Also here: Wikipedia

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman