Let's first calculate the roots of f(x) = x³-18x²+101x-180
a) f(4) = 4³ - 18.(4²) +101.(4) -180 =0, then x=4 is a root.
b) to find the 2 other roots divide x³-18x²+101x-180 by (x-4) = x²-14x+45
c) this quadratic equation has the following roots: x=5 and x=9. Hence:
f(x) = x³-18x²+101x-180 = (x-4)(x-5)(x-9)
the x-intercepts are x₁ = 4, x₂ = 5, x₃ = 9.
To find the y intercept plug x= 0 in f(x) = x³-18x²+101x-180
f(x) = y = -180 (y intercept
The graph starts from - ∞ to + ∞ and passes through one maximum and one minimum