Question

write the equation of a different polynomial function that has the same key characteristics. Explain your thinking.

Answer 1

As given by the question

There are given that the graph of polynomial function;

Now,

From the given graph, the x-intercept is:

$x=-2,\text{ -1, 0}$

Then,

The equation of the given polynomial graph is:

$y=(x+2)(x+1)(x-0)$

Then,

From the above equation:

$\begin{gathered} y=(x+2)(x+1)(x-0) \\ y=x(x+2)(x+1) \\ y=x(x^2+x+2x+2) \\ y=x^3+x^2+2x^2+2x \\ y=x^3+3x^2+2x \end{gathered}$

Hence, the equation of the given graph is shown below:

$y=x^3+3x^2+2x$