Final answer:
To determine the value of 'r' in the given cubic equation with a y-intercept of (0,12), we set x to 0 and solve for r, which results in r being equal to 0.5.
Step-by-step explanation:
To find the value of r in the cubic function y=(x+8)(x−3)(x−r), where the function has a y-intercept of (0,12), we simply substitute x with 0 and set y equal to 12, then solve for r:
12 = (0+8)(0−3)(0−r)
12 = (8)(-3)(-r)
12 = 24r
r = 12 / 24
r = 0.5
Thus, the value of r is 0.5.