Question

What is the equation of the following graph? Use ^ for exponents. Use parenthesis where necessary.

MEDAL AWARD! PLEASE HELP! GRAPH BELOW!!!

Answer 1

@seraphic_topaz

Answer 2

@NoelGreco

Answer 3

@ineedhelpnow08

Answer 4

@Loser66

Answer 5

PLEASEEE ):

Answer 6

Do you have answer options to go with this graph?

Answer 7

@jdoe0001

Answer 8

no i dont ): free response

Answer 9

please help i need it asap

Answer 10

it 's hyperbola with center (1,2)

Answer 11

give me few second, I have to look up at my note, cannot give you a wrong answer

Answer 12

thanks @jdoe0001 take it over, please

Answer 13

thanks.

Answer 14

it's a hyperbola
let's take a peek at the vertices, the "humps" coordinates

(-4, 2) and (6, 2)

the distance between both points is, well, from -4 over the x-axis to the 6, is 10 units
the "a" component will be half of that, so
a = 5

looking at the green rectangle, smaller side is the length of the "conjugate axis"
which is where the component "b" is
looking at the distance over the y-axis, it goes from 0 to 4, so is 4 units long
"b" component will be half that, so
b = 2

the center of the hyperbola will be half-way between the vertices of either axis
so moving from the vertex on the left, at (-4, 2) by 5 units, "a" value
we'd end up at (1, 2)
so the center is at
(1, 2)

Answer 15

but how do i put that into a equation for the graph?

Answer 16

keeping in mind that this hyperbola is opening over the x-axis, or is horizontal
so the fraction with the "x" variable will be the POSITIVE one
thus the equation for the hyperbola will be \(\bf
\cfrac{(x-h)^2}{a^2}-\cfrac{(y-k)^2}{b^2}=1\)

Answer 17

your center at (h, k) of course

Answer 18

what is a and b then?

Answer 19

ohhh 5 and 2?

Answer 20

yes

Answer 21

What is the equation of a parabola with vertex (0, 0) and directrix x = -3. could you help me with this one?

Answer 22

@jdoe0001

Answer 23

Is there a name for the green rectangle? How do I typically identify it in a similar problem?

Answer 24

hmm so, the vertex is the origin
and the directrix is -3
that means the focus is the opposite end, th same distance as the directrix, that is