Question

Write a cubic function with the three open blue points as roots

Answer 1

Okay, here we have this:

Considering the provided points, we are going to write a cubic function with these points as roots, so we have this:

The factored function will be equal to the multiplication of three binomials, where the first term will be x and the second will be each root with an inverse sign. Then we have:

`f(x)=\mleft(x+2\mright)\mleft(x-2\mright)\mleft(x-6\mright)`

Now we are going to operate each term to obtain the expanded function:

`\begin{gathered} f(x)=x^2x+x^2\mleft(-6\mright)-4x-4\mleft(-6\mright) \\ f(x)=x^3-6x^2-4x+24 \end{gathered}`

The last one we write is the function we are looking for and satisfies the requested roots.