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
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:
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:
`=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.