Question

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

Answer 1

F(x) = (x+1)(x+2)(x+3)

Answer 2

Answer:

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

Step-by-step explanation:

Each intercept in the graph is a factor of the equation. When the intercept has a multiplicity of 1 (to the 1st power, or normal), it simply goes through the point, and when it has a multiplicity of 2 (to the 2nd power), it curves back.

Because the graph simply passes through all 3 intercepts, and the graph shown is a cube ($x^{3}$ graph, we know that there has to be 3 factors, all with a multiplicity of 1. Multiplicity in the equation is simply the power that the factor is raised by.

If you multiply all the intercepts together [or (x - 1)(x - 2)(x - 3)], you will have the equation already in factored form, meaning you have your answer.

Hope this helped! :)