Answer:
y = x^2 - 4
Step-by-step explanation:
The vertex of a parabola is exactly halfway between the focus and the directrix. If the focus is at (0, -6) and the directrix is the line y = -2, then we do this to locate the vertex: Draw a vertical line through (0, -6) also crossing the line y = -2. The y value halfway between y = -6 and y = -2 is y = -4, and the vertex is thus (0, -4).
Using the vertex method, write out the equation of this parabola, starting with the general form y - k = (x-h)^2, where (h, k) is the vertex. Here h = 0 and k = -4
We get: y + 4 = (x - 0)^2, or y + 4 = x^2, or y = x^2 - 4. As a check, let x = 0; y = -4, which is the y-coordinate of the vertex.
Like I said above, There were 40 rolls, 6 of which were a two (6/40) and 8 of which were a 4 (8/40). Simply add these together to get 14/40 as the probability of rolling a 2 or 4. This simplifies to 7/20
first off let's notice that hmmm the vertex is above the point (3,-3), so if we "assume" is a vertical parabola, then it'd be opening downwards.... anyhow that said, let's plug in those values.
![\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Bvertical%20parabola%20vertex%20form%7D%20%5C%5C%5C%5C%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22a%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22a%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\bf vertex~~(\stackrel{h}{2}~~,~~\stackrel{k}{1})\qquad \implies \qquad y = a(x-2)^2+1 \\\\\\ \stackrel{\textit{we also know that }}{(3~~,~~-3)} \begin{cases} x = 3\\ y = -3 \end{cases}\qquad \implies -3=a(3-2)^2+1 \\\\\\ -3=a(1)^2+1\implies -3=a+1\implies -4=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y = -4(x-2)^2+1~\hfill](https://tex.z-dn.net/?f=%5Cbf%20vertex~~%28%5Cstackrel%7Bh%7D%7B2%7D~~%2C~~%5Cstackrel%7Bk%7D%7B1%7D%29%5Cqquad%20%5Cimplies%20%5Cqquad%20y%20%3D%20a%28x-2%29%5E2%2B1%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bwe%20also%20know%20that%20%7D%7D%7B%283~~%2C~~-3%29%7D%20%5Cbegin%7Bcases%7D%20x%20%3D%203%5C%5C%20y%20%3D%20-3%20%5Cend%7Bcases%7D%5Cqquad%20%5Cimplies%20-3%3Da%283-2%29%5E2%2B1%20%5C%5C%5C%5C%5C%5C%20-3%3Da%281%29%5E2%2B1%5Cimplies%20-3%3Da%2B1%5Cimplies%20-4%3Da%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20y%20%3D%20-4%28x-2%29%5E2%2B1~%5Chfill)
Answer:
11m+n
Step-by-step explanation:
Answer:
A=90
B=-20
Step-by-step explanation:
you can see the arrow in A and B
