Question

HELP MEDAL!
Using a directrix of y = -3 and a focus of (2, 1), what quadratic function is created?

Answer 1

@jim_thompson5910

Answer 2

@UnkleRhaukus

Answer 3

@freckles

Answer 4

I like deriving the equation for the parabola each time
The distance between the point (x,y) to (2,1) should have the same distance between (x,y) to (x,-3)
This is because the definition of a parabola says for all points (x,y) on the parabola we should have the distance between (x,y) to the focus is the same as (x,y) to the directrix

Answer 5

Use the distance formula to find the distance between (x,y) and (2,1)
and use the distance formula to find the distance between (x,y) and (x,-3)

Answer 6

so how do you do that

Answer 7

directrix of y = -3
focus of (2, 1)

Immediately, you should see:

vertex: (2,-1)
"p": 2

Now, just write down the equation.

Answer 8

how i dont get this part?

Answer 9

@tkhunny

Answer 10

Vertex form of a parabola is what? Write it out.

Answer 11

y=a(x-h)^2+k

Answer 12

Okay, fine. That is the Vertex Form, but that is not the way to go about it. Not enough information about "a".

The "Conic" form is this.

4p(y-k) = (x-h)^2

h and k are exactly the same as in the Vertex From.
p is the distance from Vertex to Focus or the same distance from Vertex to Directrix.

Note: This new "4p" from the conic form is the same as 1/a from the Vertex Form.

Answer 13

f(x) = one eighth (x - 2)2 - 1
f(x) = -one eighth (x + 2)2 - 1
f(x) = one half (x - 2)2 + 1
f(x) = -one half (x + 2)2 - 1 any of these

Answer 14

@tkhunny

Answer 15

@freckles got any help

Answer 16

do you want to derive the equation with the distance formula
or just use what tk said

Answer 17

the p should equal the distance between the vertex and directrix
and the sign of p should be determined by if the parabola is faced up or down

Answer 18

vertex falls halfway between the directrix and the focus