Question

could someone tell me the answer to this question please
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

I'm going to assume that's f(x) = (x^2)(x+2) = x^3 + 2(x^2).
a) so for the Leading Coefficient Test you need to determine two things: if the function is odd or even and the sign of the coefficient. The term with the highest power is x^3, so it's an odd function, meaning the ends go in opposite directions, and the coefficient is 1, which is positive. So the ends go towards positive infinity as x approaches positive infinity and they approach negative infinity as x approaches negative infinity.

Answer 2

b) To find the x intercepts u set f(x) = 0; \[x^{2}(x+2) = 0\rightarrow x^{2} = 0, x+2=0\rightarrow x = 0,-2\]
To check if they cross the x-axis, you have to check their multiplicities. The x-intercept 0 comes from x^2, so its multiplicity is 2. The x-intercept 2 comes from (x+2), so its multiplicity is 1. If the multiplicity is even, the function stays on the same side, if it is odd, it crosses the x-intercept.
So at x = 0, the graph touches and at x=-2, the graph crosses

C) The y-intercept means the x is equal to 0, so you just set x = 0 in the equation and solve. y = (0^2)+(0+2) = 2. So the y-intercept is 2.

Answer 3

wait i dont understand a

Answer 4

@fashionrpincesa20 what about it?

Answer 5

i don't understand exactly how to find the answer or did you already put the answer in there?

Answer 6

Is this the function under consideration: f(x) = x^2

Answer 7

@fashionrpincesa20 The question asked to determine the end behavior so when x approaches infinity, the ends go towards positive infinity, and when x approach negative infinity, the ends go toward negative infinity. If you were to write this out in limit notation\[\lim_{x \rightarrow \infty}f(x) = \infty \] and \[\lim_{x \rightarrow -\infty}f(x) = -\infty \] . That would be the answer.

Answer 8

okay thank you so much