Cubic function

• Mar 13th 2011, 10:23 PM
gbooker
Cubic function
If someone could please give me some assistance with this question, it would be very much appreciated

The graph of a cubic function cuts the x axis at (a,0) and touches the x axis when x=b. It has a y intercept of (0,a^3.b^3). Find the equation of the cubic function.

All I can think of how to start would be y= (x+a)(x-b)^2

So any help would be much appreciciated
• Mar 13th 2011, 10:25 PM
Prove It
It's actually $\displaystyle y = \alpha(x - a)(x - b)^2$.

Now substitute the coordinate of your $\displaystyle y$ intercept to solve for $\displaystyle \alpha$.
• Mar 13th 2011, 10:38 PM
gbooker
Quote:

Originally Posted by Prove It
It's actually $\displaystyle y = \alpha(x - a)(x - b)^2$.

Now substitute the coordinate of your $\displaystyle y$ intercept to solve for $\displaystyle \alpha$.

ok thanks, now when i substitute it in, I'm not sure if my solving is right but i get that it equals -a^2.b

Would that be right?
• Mar 13th 2011, 10:41 PM
Prove It
Yes.

So your function is...
• Mar 13th 2011, 10:44 PM
gbooker
Quote:

Originally Posted by Prove It
Yes.

So your function is...

y= -a^2.b (x-a)(x-b)^2
• Mar 13th 2011, 10:46 PM
Prove It
Quote:

Originally Posted by gbooker
y= -a^2.b (x-a)(x-b)^2

Correct.