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).inf




(b).touches at 0 and goes through -2




(c).2

Answer 1

@phi my answers are up there but my teacher said this You need to provide the end behavior. On the right, is it going up or down and also what happens on the left? Distribute the x^2 before determining the degree of the polynomial. Then use the Leading Coefficient Test. Refer to section 2-6 for examples and sample problems, here you will find how to describe end behavior. 4b. At the x intercept, y=0. Since this is quadratic, how would you know if it intercepts or touches the x-axis?

Answer 2

@Vocaloid

Answer 3

the cube function ( exponent 3) with positive leading coefficient has the left end at \(-\infty\) and right end at \(+ \infty\)

Answer 4

Hence, by looking at the leading coefficient ( the number stands right in the front of x^3) , you can see how the end looks like

Answer 5

so how would i put it into words though

Answer 6

Put as what I wrote above.

Answer 7

ohh ok

Answer 8

\(f(x) = x^2(x+2)=x^3+2x^2\)
The leading coefficient is 1 >0 , hence the graph will start at -inf and end at + inf
Dat sit

Answer 9

1>0

Answer 10

brb

Answer 11

to b) x intercepts happen when y =0, that is \(x^2 (x+2) =0\) , solve for x, you will have 2 solutions. Those are x-intercepts.

Answer 12

y-intercepts happen when x =0, replace x =0 to solve for y