Question

need help with Algebra 2 (will FAN & MEDAL)

Answer 1

write an equation of a parabola with the given focus and directrix.
focus: (-2,0);directrix: x=4

Answer 2

no one likes these conic section question but they are not that hard if you know a couple things
do you know what this looks like?

Answer 3

ok lets go slow, but not that slow
\(x=4\) is a vertical line right (not horizontal like say \(y=4\))

Answer 4

yes

Answer 5

this is where you say "yes i know that "

Answer 6

ok good

Answer 7

lol i do know that

Answer 8

so lets graph the line \(x=4\) and also plot the point \((-2,0)\)

Answer 9

NOW do you know what it looks like?
opens left, right, up or down?

Answer 10

ok

Answer 11

left?

Answer 12

yes

Answer 13

(0,-2)?

Answer 14

next we need to know the vertex, which is half way between the focus and the directrix
what is half way between them

Answer 15

look at the picture and visualize the point half way between the focus and the directrix
your answer should be a coordinate, not a number
also not \((0,-2)\)

Answer 16

1,0

Answer 17

yes

Answer 18

so now we know it looks like \[y^2=-4p(x-1)\] and that since general form is \[(y-k)^2=4p(x-h)^2\]and you have \((h,k)=(1,0)\)

Answer 19

the minus sign because it opens to the left

Answer 20

also that is the reason the \(y\) term is squared, not the \(x\) term
all you need it \(p\)

Answer 21

\(p\) is the distance between the focus and the vertex, or the vertex and the directrix, which you pretty much know already

Answer 22

no \(p=3\)

Answer 23

so \[y^2=-12(x-1)\]

Answer 24

i see i made a typo above
there is not square on the x term

Answer 25

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

Answer 26

the distance between \((-2,0)\) and \((1,0)\)

Answer 27

or from \((1,0)\) to \((4,0)\) same distance

Answer 28

ok

Answer 29

\[y ^{2}=-12x+12 \]

Answer 30

\[x=\frac{ -1 }{ 12 } y^2+1\]

Answer 31

thank you