anonymous
  • anonymous
Find an expression for a cubic function f if f(3) = 108 and f(-3) = f(0) = f(4) = 0.
Mathematics
chestercat
  • chestercat
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dumbcow
  • dumbcow
y = ax(x+3)(x-4) find a by using point (3,108)
anonymous
  • anonymous
how did you get that
dumbcow
  • dumbcow
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

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anonymous
  • anonymous
thanks a million times
dumbcow
  • dumbcow
your welcome glad to help

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