find the following for f(x)=(x+6)^2(x-2)^2 x and y intercepts of the polynomial power function that the graph of f resembles for large values /x/must show work

1 Answer | Add Yours

lfryerda's profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted on

The x-intercepts of a function are found by setting y=0 and solving for x.  In this case the function is in fully factored form, which means that we can find the x-intercepts by solving:

`0=(x+6)^2(x-2)^2`   set each factor to zero

so the x-intercepts are x=-6 and x=2.

The y-intercept is found by setting x=0 and solving for y, which gives:

`y=(6)^2(-2)^2`

`=36(4)`

`=144`

The y-intercept is y=144.

For large values of x, the function resembles the polynomial of the highest degree.  

If we expand out the function, we get:

`f(x)=(x+6)^2(x-2)^2`

`=x^4+` lower degree terms

So for large values of x, the function resembles `y=x^4` .  The x-intercepts are x=-6 and x=2.  The y-intercept is y=144.

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question