Question

Write the general form of the equation which matches the graph below. In complete sentences, explain the process taken to find this equation.

Answer 1

thats the graph

Answer 2

parabola eh; y^2 = 4ax if i recall correctly

Answer 3

that will of course have to be modified to this particular graph

Answer 4

a is equal to the value of x at that dotted line; cant tell what it is from here tho

Answer 5

and since x is always negative; that means its gonna be a -y^2

Answer 6

it says i have to put it in x=a(y-h)^2-k format

Answer 7

right, but lets get this format right before we try to shift things about

Answer 8

-y^2 = 4ax

x = -\(\cfrac{1}{4a}\) (y-3)^2 is what it looks like to me

Answer 9

i cant tell the value for a; what does the dotted line cross at?

Answer 10

it crosses at 4,0

Answer 11

if that right, then that denom is 16

Answer 12

so the final equation is x=1/16(y-3)^2?

Answer 13

id say yes; except for make it a negative on your fraction

Answer 14

x is always negative in this graph so you have to put it in there

Answer 15

okay thank you so much

Answer 16

youre welcome

Answer 17

thnx

Answer 18

2 years ago eh ... and sure, youre welcome :)

Answer 19

@amistre64

Answer 20

you wanted to know how we get: x=-1/4a(y-3)^2

Answer 21

the way i find these has changed over the years

Answer 22

since the graph opens to the left, then we know this is going to have
to be part of some x = -y^2 setup

but when y=3, we want x to be 0; so we modify it as:

x = (y-3)^2

the only thing left to do is to determine how to spread it out, in general, the point directly across from the focus will help us out