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- Barrelracing

What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6?
a) -1/6x^2 +4/3x + 11/6
b) 1/6x^2 - 4/3x - 11/6
c) 3/50x^2 + 11/25x + 3/5
d) 2/50x^2 + 11/25 + 2/5

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- Barrelracing

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- freckles

|dw:1444325601632:dw|
the vertex is halfway between the directrix and the focus

- freckles

what number is midway between -3 and -6?

- Barrelracing

-4 and -5

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- freckles

but what number is midway between -3 and -6?
hence do you know how to find the average of -3 and -6?

- Barrelracing

oh no i dont

- freckles

the average of two numbers is the sum of the numbers divided by 2

- Barrelracing

i got -1.5

- freckles

-3+(-6)=-9
-9/2 equals -4.5 not -1.5

- Barrelracing

oh i did wrong sorry

- freckles

-4.5 makes since because this number is halfway between -4 and -5

- freckles

sense*

- freckles

it is also the number halfway between -3 and -6

- freckles

|dw:1444325972949:dw|

- freckles

so our parabola looks like this roughly :
|dw:1444326013448:dw|

- freckles

anyways the equation is
\[4p(y-k)=(x-h)^2 \\ \text{ where } (h,k) \text{ is the vertex } \\ \text{ and } p \text{ is the distance between the vertex and the focus } \\ \text{ we also have } p>0 \text{ here since the vertex is above the directrix } \\ \text{ if it was the other way around we would have } p<0\]

- Barrelracing

ok thank you i get it now

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