Question

Can someone please help! Find the focus of the parabola that has vertex (-4,-1), opens vertically, and passes through the point (-3,4).

Answer 1

ok for a given parabola
\[y = a(x-h)^{2} +k\]
the focus is \[(h , k+ \frac{1}{4a})\]
you are given the vertex (h,k) , you can solve for "a" using point (-3,4)

Answer 2

just unsure of how to work (-3,4) into the problem.. hmm

Answer 3

(-4,-15/16) ?

Answer 4

nope it must be (-4,-19/20)... but why did I get -15/20? hmm

Answer 5

-15/16 i mean

Answer 6

oh you substitute (-3,4) as (x and y in parabola equation

--> 4 = a(-3+4)^2 -1

solve for a

Answer 7

right and i get 4

Answer 8

hmm
4 = a(1)^2 -1
4 = a-1
5 = a

Answer 9

ohh i was getting 1^2-1=0 ... but i get it now

Answer 10

so -19/20 got it! thanks!

Answer 11

yw