<u>ANSWER</u>

<u>EXPLANATION</u>
The given function is

We make the coefficient of
unity by factoring
out of the last two terms to obtain;

We now add and subtract half the coefficient of
multiplied by a factor of 6 to obtain;

We now factor 6 out of the last two terms to get;


The quadratic trinomial in the parenthesis is now a perfect square.

Hence the vertex form of the polynomial is

If Z is the unknown, then
Z-(-3/4)= 6 1/2
Z+3/4= 6 1/2
Z= 6 1/2 - 3/4
Z= 23/4 = 5 3/4
Answer:
Vertical A @ x=3 and x=1
Horizontal A nowhere since degree on top is higher than degree on bottom
Slant A @ y=x-1
Step-by-step explanation:
I'm going to look for vertical first:
I'm going to factor the bottom first: (x-3)(x-1)
So we have possible vertical asymptotes at x=3 and at x=1
To check I'm going to see if (x-3) is a factor of the top by plugging in 3 and seeing if I receive 0 (If I receive 0 then x=3 gives me a hole)
3^3-5(3)^2+4(3)-25=-31 so it isn't a factor of the top so you have a vertical asymptote at x=3
Let's check x=1
1^3-5(1)^2+4(1)-25=-25 so we have a vertical asymptote at x=1 also
There is no horizontal asymptote because degree of top is bigger than degree of bottom
There is a slant asympote because the degree of top is one more than degree of bottom (We can find this by doing long division)
x -1
--------------------------------------------------
x^2-4x+3 | x^3-5x^2+4x-25
- ( x^3-4x^2+3x)
--------------------------------
-x^2 +x -25
- (-x^2+4x-3)
---------------------
-3x-22
So the slant asymptote is to x-1
<span>Analogicaly as in the previous question - firstly let's find the common denominator for those fractions:
2/3 = 12/18
2/9 = 4/18
5/6 = 15/18
11/18 = 11/18 :)
From the least to the greatest:
2/9, 11/18, 2/3, 5/6</span>