1. ## Minimise A= 1/2(1-x+qx^2)

Hey, got a question, my sis has exams tomorrow and she cant solve this,...its been 7 years ive done this lvl of maths, and dont remember enough to help her...any help ?

Its part of the question

Show A= 1/2(1-x+qx^2)

Given that x can vay, show that Qy=Yr when A is a min and express the min of A in terms of q

First part she did, now 2nd part

I forgot, PQRS is a square

2. A is the area of triangle sxy, and q is a constant...

Still dont get it

Btw, its an o level question for may 02

3. sorry, some info was missing in the first diagram

4. $\displaystyle (1/2)(qx^2- x+ 1)$ is quadratic. You can rewrite it as $\displaystyle (q/2)(x^2- (1/q)x+ 1/q)$ and complete the square: $\displaystyle (q/2)(x^2- (1/q)x+ (1/4q^2)- (1/4q^2)+ 1/q= (q/2)(x- 1/2q)^2+ (4q-1)/4q^2$. Since a square is never negative, this will be a minimum (assuming q is positive) when x= 1/(2q) and that minimum will be $\displaystyle (4q-1)/(4q^2)$.

5. Thanks, have been able to solve it