Write the equation of a hyperbola with vertices (0, -2) and (0, 2) and co-vertices (-4, 0) and (4, 0).
y squared/16 minus x squared/4 equals 1
x squared/4 minus y squared/16 equals 1
y squared/4 minus x squared/16 equals 1
x squared divided by 16 minus y squared divided by 4 equals 1

C. y squared/4 minus x squared/16 equals 1

Step-by-step explanation:

Given that vertices of hyperbola are (0,-2) and (0,2)  and

Co-vertices of hyperbola as (-4,0) and (4,0)  then a sketch will show you that this hyperbola has its transverse axis on the y-axis and has its center at the origin (0,0)

This means that the standard equation for the hyperbola should follow;

Using the coordinates of the vertices, you can find the length of the transverse axis and the value of a as;

(0,-2) and (0,2) , 2--2=4

2a=4

a=4/2=2

a=2

Using the coordinates of the co-vertices, you can find the length of the conjugate axis as;

(-4,0) and (4,0) ⇒ 4--4=8

2b=8

b=8/2=4

b=4

substitute values in equation as;

a negative exponent is translated as follows:

so, we have

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1