Question

Write the equation of the graph shown in factored form.

Answer 1

let's take a peek at the graph.

the graph of the equation touches the x-axis at 1, 2 and 3, at 1 it crosses it, at 2 it crosses it, at 3 is doesn't cross it, it simply bounces off of it.

on the roots/solutions the graph crosses the x-axis, they have ODD multiplicity, on the solutions it bounces off of it, they have EVEN multiplicity, so then.

x = 1 => x - 1 = 0  <------ one  factor

x = 2 => x - 2 = 0 <------ another factor

x = 3 => x - 3 = 0  <------ another factor, BUT with even multiplicity

(x-1)¹(x-2)¹(x-3)² = f(x)

(x-1)(x-2)(x-3)² = f(x).