Can you find the focus of this small parabola?? :)

Question

anonymous · Answer

attachment

accessdenied · Answer

If my memory serves me, the distance from the vertex to the focus of a parabola can be found from the form $y = a(x - h)^2+k$ as $\displaystyle p = \frac{1}{4a}$

accessdenied · Answer

That would place the focus at the point $(h, \; k+ p)$
  --> The parabola is concave-up, so the focus is above the vertex.
  --> It's directly above the vertex, so the horizontal value is the same as the vertex's.

anonymous · Answer

so (2, 4+1/4a) ? Im sorry I dont get how to get  the y part :/

accessdenied · Answer

well the a-value is just whatever is multiplied onto (x - h)^2.
In this case, it's a = 1/8
y-value = 4 + 1/(4*1/8)

Also, it'd be -2 for the same reason as the circle problems.  The general form has a (x - h)^2, so (x + 2)^2 = (x - -2)^2

anonymous · Answer

well 4*1/8 is 1/2...
so 4 + 1/1-2 or .5?

anonymous · Answer

which is 6 :)

anonymous · Answer

-2,6

accessdenied · Answer

Yeah.  :)

anonymous · Answer

Honestly. you're amazing. lol