Write an equation for the 4th degree polynomial graphed below. use k if your leading coefficient is positive and −k if your leading coefficient is negative. use y for the dependent variable. you can leave your answer in factored form.

Solution-

General 4th degree polynomial equation with roots as a, b, c, d is,

If the graph touches or bounces on a root, then that root has an even multiplicity.

If the graph goes through a root, then that root has an odd multiplicity.

Here, the roots are -1, 2, 4. (∵ as the graph crosses or touches x-axis or y=0 line)

At x=2, the graph touches the x-axis, so it has a multiplicity of 2

Now, we have to consider the end behavior or leading co-efficient.

and

So, the graph must be function with even degree and negative leading co-efficient.

So, the final equation becomes,

3100

step-by-step explanation: