Question

Complete the following:
(a) Use the Leading Coefficient Test to determine the graph's end behavior.

(b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis

and turns around at each intercept. Show your work. (c) Find the y-intercept. Show your work.

f(x) = x2(x + 2)

(a).
(b).
(c).

Answer 1

so, what is the leading coefficient test?

f(x) = x^2 (x+2)
if f(x)=0, then you must have either
x^2 = 0
or (x+2) = 0

Note that x^2 is always positive. SO, at x=0, the graph touches the x-axis from above, then goes up again

at x = -2, f(x) changes sign from - to +, so the graph crosses the x-axis.

In general,
f touches at even powers of roots
f crosses at odd powers

I figure you can find y when x=0 for the y-intercept.

This is pretty basic stuff, mostly Algebra I. Better review the pertinent sections in your text.