Determine equation of the cubic function?

Question

The zeros of a cubic function are x = -2, 3 and 2/5. The function has a y-intercept of 6. Determine equation of the cubic function I'm not quit sure how to get this without given points which it passes for? Is it asking to solve for a? 6=a(x+2)(x-3)(x-2/5) ??

Answer 1

Is it asking to solve for a?  6 = a(x+2)(x-3)(x-2/5) ??

Yes! for when x = 0.

You have an equation y = f(x).

When it says, "y has an intercept of 6", then that means that y = 6 when x = 0, i.e. y = f(0) = 6.

So, 6 = a(0 + 2)(0 - 3)( 0 - 2/5)

6 = a*(12/5)

a = 5/2

Therefore y = (5/2)(x + 2)(x - 3)(x - 2/5)

This should be multiplied out to show a cubic polynomial and simplified.