Answer: 1) Vertex: (6, -2) Focus: (6, -7/4) Directrix: y = -9/4
2) Vertex: (-2, -1) Focus: (-7/4, -1) Directrix: x = -9/4
<u>Step-by-step explanation:</u>
Rewrite the equation in vertex format y = a(x - h)² + k or x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.
- (h, k) is the vertex
- p is the distance from the vertex to the focus
- -p is the distance from the vertex to the directrix

1) y = x² - 12x + 34


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2) x = y² + 2y - 1


You can find the slope either by just looking at the line or using the slope formula.
#1: The slope formula is:
Find two points and plug it into the formula
I will use (0, 2) and (1, -1)
(0, 2) = (x₁, y₁)
(1, -1) = (x₂, y₂)

[two negatives cancel each other out and become positive]

m = -3
#2: To find the slope without having to do the work, you use this:

Rise is the number of units you go up(+) or down(-) from each point
Run is the number of units you go to the right from each point
If we start at a defined/obvious point, like (0, 2), find the next point and see how many units it goes up or down and to the right. The next point is (1, -1), so from each point, you go down 3 units and to the right 1 unit. So your slope is -3/1 or -3. You can make sure the slope is right by looking at another point.
Step-by-step explanation:
Given the geometric sequence
8 + 6 + 4.5...
A geometric sequence has a constant ratio and is defined by























∵ 


∵
, 
so
∵ 

∵ 
∵ 
Therefore, the sum of the first 25 terms in this geometric series: 31.98
Answer:
Im going to guess k is the unknown
Step-by-step explanation:
7k-14=42
42+14=7k
56=7k
56/7=k
k=8
The answer is the answer is C and F.
This is found by inserting the equation above into the quadratic formula or -b plus or minus the square root of b^2 - 4ac over 2a.
With that, you find that the first number is a -3, which eliminates choices B and D.
Then, solving the 4ac portion, you find that inside the square root the number is 29, which gives you the last two answer choices.
Hope this helps!