Question

Analyze the graph of the following function as follows:

(a) Find the x- and y-intercepts.

(b) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.

(c) Find the maximum number of turning points.

(d) Graph the function

Please show all of your work.
f(x)=x^2(x+2)

Answer 1

is this
\[f(x)=x^2(x+2)=x^3+2x^2\]?

Answer 2

zeros are

\[x=0,x=-2\]

Answer 3

end behaviour looks like x^3 so goes to infinity as x does, and minus infinity as x goes to minus infinity

Answer 4

degree is 3 so it can have at most two turning points

Answer 5

and y - intercept is what you get when x = 0, namely 0

Answer 6

Given Equation:
\[x ^{2}(x+2)\]
Which is,
\[x ^{3}+2x ^{2}\]
So our equation becomes,
\[F(x)=x ^{3}+2x ^{2}\]
Or, \[Y=x ^{3}+2x ^{2}\]

1) Finding the x-intercepts and y-intercepts.
Now, x-intercept: The point at which the graph cuts the x-axis.
To find the x-intercept,
Take Y=0
So,
\[0=x ^{3}+2x ^{2}\]
Take 2x^2 to other side,
\[-2x ^{2}=x ^{3}\]
Cancelling x^2 and x^3 from both sides, we are left with:
\[-2=x\]
So the x-intercept is -2.

Finding the y-intercept:
Y-intercept: The point at which the graph cuts the y-axis.
So, to find the y-intercept, take x=0
So,
F(x)=F(0):
\[(0)^{3}+2(0)^{2}\]
Which ultimately gets us 0.
So the y-intercept is 0.
So we get the coordinates of the point as (-2,0)
The graph should be something like this...

2.I didn't understand sorry...
3. There are no turning points, it is a straight line, so 0 turning points.
4.Graph attached.

Please do ask if you need any more help! :D

Answer 7

@satellite73 has given you all the required information - you just need to graph it now.

Answer 8

Correction: there can be 3 turning points like Satellite73 said, I didn't notice the degree earlier sorry.

Answer 9

how is the graph supposed to go can someone show me please?