Question

Must show work! Find vertex, foci, directrix for (y-7)^2=-12(x+1)

Answer 1

\(\large {\begin{array}{llll}
(y&-{\color{red}{ k}})^2=&\ {\color{green}{ 4p}}(x&-{\color{blue}{ h}})\\
&\ \uparrow &\ \uparrow \\
(y&-{\color{red}{ 7}})^2=&-{\color{green}{ 12}}(x&{\color{blue}{ +1}})
\end{array}\\ \quad \\
vertex=(h,k)\\
p=\textit{distance form the vertex to the focus or directrix}}\)

Answer 2

whats the answer though?

Answer 3

well, what's the vertex?

Answer 4

(1,7)

Answer 5

(-1,7)

Answer 6

sorry, I just happen to be a bit lagged =(

Answer 7

so the vertex is at (-1, 7)

and we know that -12 = 4p so what would be the "p" distance?
well \(\bf -12=4p\implies -3=p\)

so.... the negative means the graph is flipped the other way of the usual

so.... notice we have a "squared y-coordinate" value
that means the parabola is a horizontal one

usually the positive one goes to the right
so a negative number in front of the "p" means is opens or goes to the left

Answer 8

what are the foci?

Answer 9

so the "p" is the distance form the vertex to the focus or directrix

so p=3, so