end behaviour and zero behavior of polynomial graph?

Question

of y=-3(x-2)(x=2)^2(x-3)^2


...end and zero

for end i just put it goes down from quad 3 and goes down (finish) in quad 4..can i do that?....what about zero?

Answer 1

This polynomial has degree 5 (I think you meant a plus rather than = with the (x=2) ).

Since the leading coefficient is negative (-3), the end behavior goes to positive infinity in quadrant II meaning it goes up and to negative infinity in quadrant IV meaning it goes down. Odd degree and negative leading coefficient has end behavior like -x^3 if you know what that looks like.

To find the zeros, just set each term that has a x to zero and solve. Note that -3 is NOT a zero. x-2=0 so x=2, x+2=0 so x=-2, x-3=0 so x=3.

Answer 2

Assuming your factor (x=2) should be (x+2), then the poly is 5th degree with a -3 coefficient, which means in any reasonable window it starts in quad 2 and ends in quad 4 (goes from high left to low right).

When x = 0, of course y = 0.

The zeros are given by the factors, single zero at x = 2, double at x = -2, double at x = 3.

Answer 3

This is the kind of problem that I recommend taking a step back for the 'big picture'

Determine the order of the poly by adding all those exponents: you get 5, and odd number. This means that the poly is anti-symmetrical.: that is goes quad 3 to quad 1 or quad 2 to quad 4.

Now look a the coeffiecient of the largest x^5: it's -3

Together they tell you the behavour for large negative and large postive values of x

Large negative x gives large negative x^5, now multiplied by -3 gives large positvie values of the poly, that is quad 2

Large positive x gives large positive x^5, times -3 gives quad 4 behaviour.

So, it goes from quad 2 to quad 4.

Answer 4

The graph will dip from an asymptote, point off, dip right into a bucket, dip right into a very deep bucket then upward thrust to an asymptote. bypass to the internet internet site bellow, put in the equation into the functionality and then zoom in. whilst y = 0, x = -2, 0 and 3