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#1 2007-04-12 15:44:06

JClarke
Member
Registered: 2007-04-12
Posts: 1

Quadratic Functions!

Ahhhh, I have a test tomorrow and I'm having a lot of trouble figuring out these questions, can you please help?

(1) Find two numbers whose difference is 10 and whose product is a minimum.

(2) Determine the maximum area of a triangle, in square centimetres, if the sum of its base and height is 10 cm. 

(3) Find the value of q so that quadratic equation y=-3(x+2)^2 + q passes through this point.

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#2 2007-04-12 16:06:21

JClarke
Member
Registered: 2007-04-12
Posts: 1

Re: Quadratic Functions!

Even if you can only help me with one question, I'm in big trouble!!!

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#3 2007-04-12 16:58:27

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Quadratic Functions!

(1) Let the numbers be x and x+10. Then their product is y = x(x+10). Now apply calculus.

(2) If the base is x, the height is 10−x. The area is y = ½x(10−x). Apply calculus again.

(3) What point?

Last edited by JaneFairfax (2007-04-12 16:59:07)

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#4 2007-04-12 21:55:04

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,664

Re: Quadratic Functions!

1) x(x+10) = x²+10x, the derivative is 2x+10, set it to zero (for a minimum or maximum) and you get x = -5. The product is -25, which I would hazard a guess is the minimum.

That is easiest for me, but you could also solve it using Completing the Square:

x²+10x  =>  (x+5)² - 25, and that indicates the point (-5,-25) as a vertex (turning point).


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

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