Answer: 1. x = (y - 2)² + 8

3. y = 2(x +9)² + 7
<u>Step-by-step explanation:</u>
Notes: Vertex form is: y =a(x - h)² + k or x =a(y - k)² + h
- (h, k) is the vertex
- point of vertex is midpoint of focus and directrix:


- p is the distance from the vertex to the focus
1)

Now let's find the a-value:

Now, plug in a = 1 and (h, k) = (-8, 2) into the equation x =a(y - k)² + h
x = (y - 2)² + 8
***************************************************************************************
2)

Now let's find the a-value:

Now, plug in a = -1/2 and (h, k) = (1, 10) into the equation x =a(y - k)² + h

***************************************************************************************
3)

Now let's find the a-value:

Now, plug in a = 2 and (h, k) = (-9, 7) into the equation y =a(x - h)² + k
y = 2(x +9)² + 7
Taylor series is 
To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have
f(x) = ln(x)

.
.
.
Since we need to have it centered at 9, we must take the value of f(9), and so on.
f(9) = ln(9)

.
.
.
Following the pattern, we can see that for
,
This applies for n ≥ 1, Expressing f(x) in summation, we have

Combining ln2 with the rest of series, we have

Taylor series is 
Find out more information about taylor series here
brainly.com/question/13057266
#SPJ4
18 . it's increasing by 5 every time so the next one after 23 is 28