Question

find the following for the function
f(x)= (x+5)^2(x-1)^2
a) find the x and y intercepts for the polynomial function f
b) determine whether the graph of f crosses or touches the x axis at each x intercept
C) put all information together to obtain the graph of f

Answer 1

The x-intercepts are the roots.
The y-intercept is at 5^2*1^2 = 25

Since the roots are of even order, the graph touches the axis at each root.

So, degree-4 polynomial with positive coefficient. Down from the left, tangent at each root, then back up to the right.