Question

Find an expression for a cubic function f if f(3) = 108 and f(-3) = f(0) = f(4) = 0.

Answer 1

y = ax(x+3)(x-4)
find a by using point (3,108)

Answer 2

how did you get that

Answer 3

when you know the zeroes of a function you can po ut it in factored form
say f(x) = x^2-4
so f(x) = (x+2)(x-2)
if you want to solve for 0 you get x = 2 and -2
in this case you are working backwards you know the x-values that make f(x)=0
(x+3) =0 when x=-3, f(-3) =0
the x in front comes from f(0)=0
the a is a scale factor which determines the shape of graph, is it skinny or wide
this is because many different graphs may have the same zeroes but only one will go through a different specific point (3,108), f(3) =108
to find the cubic equation you just need to plug in 3 for x, 108 for y and solve for a

108 = 3(3+3)(3-4)a
108 = (3*6*-1)a
108 = -18a
108/-18 = a
a = -6

y = -6x(x+3)(x-4)
expand
y=-6x(x^2-x-12)
y=-6x^3 +6x^2 + 72x

Answer 4

thanks a million times

Answer 5

your welcome
glad to help