Rewrite as y−k=a(x−h)2 or x−h=a(y−k)2. Find the vertex, focus, and directrix.
y−3=(2−x)^2

Given:

The given equation is

To find:

The vertex, focus, and directrix.

Solution:

The equation of a parabola is

    ...(i)

where, (h,k) is vertex, and directrix is

We have,

It can be written as

   ...(ii)

On comparing (i) and (ii), we get

Vertex of the parabola is (2,3).

Therefore, the focus of the parabola is .

Directrix of the parabola is

Therefore, the directrix of the parabola is .

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages