Answer:
To find the cubic function with the given roots, we can use the factored form of a cubic function:
f(x) = a(x - r1)(x - r2)(x - r3)
where r1, r2, and r3 are the roots of the function.
Substituting the given roots, we get:
f(x) = a(x + 9)(x + 5)(x - 3)
To find the leading coefficient a, we need to use the y-intercept of the function, which is given as -27.
When x = 0, the function becomes:
f(0) = a(9)(5)(-3) = -27
Simplifying and solving for a, we get:
a = -27 / (9)(5)(-3) = 0.6
Rounding to two decimal places, the leading coefficient of the cubic function is a = 0.60.