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

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).

dumbcow · Answer

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)

anonymous · Answer

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

anonymous · Answer

(-4,-15/16)  ?

anonymous · Answer

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

anonymous · Answer

-15/16 i mean

dumbcow · Answer

oh you substitute (-3,4) as (x and y in parabola equation

--> 4 = a(-3+4)^2 -1

solve for a

anonymous · Answer

right and i get 4

dumbcow · Answer

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

anonymous · Answer

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

anonymous · Answer

so -19/20  got it! thanks!

dumbcow · Answer

yw