Find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at y = + or - 1/2 x.

so, since we know the vertices are at (0, 8) and (0, -8), that means is a vertical hyperbola, or one with a vertical traverse axis, check the picture below.

which means, its center is at (0,0), and the traverse axis is 8 units long.

because the hyperbola is opening over the y-axis, that means for the equation, the fraction with the "y" is the positive one, so

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

sadsdda

step-by-step explanation: