Question from independent 2003 (1 Viewer)

[Linda N]

I never came across this question below and i need help.

Express 9x^2 + 4x + 16 in the form (Ax + 1)^2 + B(x - 2) + C

 

[Estel]

You should've come across this.
Equating coef, A=3
sub x = 2 obtain a value for C
sub x = -1/3 obtain a value for B

 

[Linda N]

What topic does this question belong? Where did u get x= 2 to subst. to get C and x= -1/3 to obtain B?

 

[Estel]

Syllabus topic 9.
Discriminant theory and quadratics.

I used x = 2 and -1/3 as they make the working out much easier.
Any other values will require the solving of simultaneous equations. Try it.

 

[KungPow]

I'm curious too. Where did you get those numbers from? Did you solve the first equation to get x values?

 

[tennille]

A is automatically 9, by comparing both sides. Then you sub in 2 to find out C. Then you can sub in 0 to find out B.

 

[smallcattle]

A is automatically 9, by comparing both sides. Then you sub in 2 to find out C. Then you can sub in 0 to find out B.

why is A automatically 9?

 

[tennille]

You dont haveto sub in any particular value to determine B, because you have already identified A and C.

 

[tennille]

Because you compare it :

9x^2 + 4x + 16 in the form (Ax + 1)^2 + B(x - 2) + C

It has to be 9, there are no other x^2

 

[tennille]

sorry, it should be 3. My bad.

 

[Linda N]

Oh.. quadratic function. Totally forgot about that. I remember doing this topic ages ago like in year 11 term 1.

 

[sf_diegoxrock]

so whats the answer? no, no, A = 9 for sure!!

i got..

(9x+1)^2 - 15 ( x-2) - 15

 

[Riviet]

so whats the answer? no, no, A = 9 for sure!!

i got..

(9x+1)^2 - 15 ( x-2) - 15

(9x)²=81x²