SOLUTION: Hi - function question.... There is the function g(x) = K(x+3)(x-3) for some constant K. If g(a-1.2) = 0 and a>0, what is the value of a? thank you - we are at a loss..

Algebra ->  Functions -> SOLUTION: Hi - function question.... There is the function g(x) = K(x+3)(x-3) for some constant K. If g(a-1.2) = 0 and a>0, what is the value of a? thank you - we are at a loss..      Log On


   

Question 336099: Hi - function question....
There is the function g(x) = K(x+3)(x-3) for some constant K.
If g(a-1.2) = 0 and a>0, what is the value of a?
thank you - we are at a loss....
Fiona
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of a if:
g%28x%29+=+K%28x%2B3%29%28x-3%29 K = some constant. and if...
g%28a-1.2%29+=+0 and a%3E0
In the given function g%28x%29+=+K%28x%2B3%29%28x-3%29 simplify.
g%28x%29+=+K%28x%5E2-9%29 For every x, replace with (a-1.2)
g%28a-1.2%29+=+K%28%28a-1.2%29%5E2-9%29%29 Expand the right side.
g%28a-1.2%29+=+K%28%28a%5E2-2.4a%2B1.44%29-9%29
g%28a-1.2%29+=+K%28a%5E2-2.4a-7.56%29 Now set this equal to zero since:g%28a-1.2%29=0
K%28a%5E2-2.4a-7.56%29+=+0 Apply the zero product rule:
K+=+0 or a%5E2-2.4a-7.96+=+0
a%5E2-2.4a-7.56+=+0 You can use the quadratic formula to solve this and you should get:
a+=+4.2 or a+=+-1.8