Question

Write the equation of the graph shown below in factored form ​

Answer 1

`f(x)=(x-3)^(2)(x-2)(x-1)`

Explanation:

we know that

The roots (or x-intercepts) of the equation are

x=1 -----> with multiplicity 1

x=2 -----> with multiplicity 1

x=3 -----> with multiplicity 2 (because is a turning point)

so

The factors are

`(x-1), (x-2), (x-3),(x-3)`

The equation is equal to

`f(x)=(x-3)(x-3)(x-2)(x-1)\\ \\f(x)=(x-3)^(2)(x-2)(x-1)`