# Thread: Find out expression of a cubic function

1. ## Find out expression of a cubic function

i have a question i have no idea how to solve.....

Find an expression for a cubic
function f if f(3) = 54 and f(-3) = f(0) = f(4) = 0.

f(x) =_________________________

Does anyone know how to solve this.

2. Originally Posted by Sneaky
i have a question i have no idea how to solve.....

Find an expression for a cubic
function f if f(3) = 54 and f(-3) = f(0) = f(4) = 0.

f(x) =_________________________

Does anyone know how to solve this.
Since you have three roots you can start by using the model $\displaystyle y = a (x - \alpha) (x - \beta) (x - \gamma)$ where $\displaystyle x = \alpha, \, \beta$ and $\displaystyle \gamma$ are the known roots of the cubic.

Then substitute f(3) = 54 and solve for $\displaystyle a$.

3. Originally Posted by Sneaky
i have a question i have no idea how to solve.....

Find an expression for a cubic
function f if f(3) = 54 and f(-3) = f(0) = f(4) = 0.

f(x) =_________________________

Does anyone know how to solve this.
they gave you the zeros ...

f(x) = kx(x+3)(x-4) , where k is some constant

and you know f(3) = 54 ... you can find out what k is

### find expression for cubic function

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