Question

PLEASE HELP Write an equation with the smallest possible degree for the function graphed attached.

Answer 1

Answer:

Below

Step-by-step explanation:

First we can go ahead and create a general equation for this polynomial

Here are our roots :

     x1 = - 3

     x2 = -1

     x3 = 1

Now because this function extends from quadrant 4 to 3, we know that this has been reflected in the x-axis :

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

However if we look closely you can see that the graph appears to "bounce" off certain roots. In this case it bounces off x = 1. This means that this root is an order of 2. It also has a weird looking curve on x = - 3 which means that this root is an order of 3.

Our general equation will look like this :

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

Now we need to sub in any point on the graph to solve for the a value. I'm just going to arbitrarily pick the y-intercept at ( 0 , -3 )

     - 3 = - a ( 0 + 3 )^3 ( 0 - 1 )^2 ( 0 + 1 )

     - 3 = - a (3)^3 (-1)^2 (1)

     - 3 = - a (27)(1)(1)

     - 3 = - a27

     1/9 = a

Here is our FINAL equation :

     f(x) = - 1/9 ( x + 3 )^3 ( x - 1 )^2 ( x + 1 )

Hope this helps! Best of luck <3

I would really appreciate a brainliest if possible :)