Create an equation for a cubic function, in standard form, that has x-intercepts given by the set {-3, 1, 7} and which passes through the point (-2, 54) .

Step-by-step explanation:

let the  function  be  f(x)=a(x+3)(x-1)(x-7)

∵ it passes through (-2,54)

54=a(-2+3)(-2-1)(-2-7)

54=a(1)(-3)(-9)

27a=54

a=2

so cubic is

f(x)=2(x+3)(x-1)(x-7)

=2(x+3)(x²-7x-x+7)

=2(x+3)(x²-8x+7)

=2(x³-8x²+7x+3x²-24x+21)

=2(x³-5x²-21x+21)

=2x³-10x²-42x+42