Answer:
1) vertex = (-2,4)
2) Focus = (-0.5,4)
3) x= -3.5
y= 4
4) y=4
Explanation:
General equation of parabola that is parallel to a-axis and vertex at (h,k) is given as
(y - k)^2 = 4p (x - h)
where
vertex of parabola is at (h,k)
focus of parabola is given at (h + p, k)
the directrix of parabola is given as x = h - p.
Now
1)
finding vertex of parabola:
Given equation of parabola
(y-4)^2=6(x+2)
Comparing with the general form, we get
h=-2 ,k=4 and 4p=6
hence vertex = (-2,4)
2)
Finding focus
Comparing with the above standard form we get
k=4, h=-2, p=3/2
Since the given parabola is parallel to x-axis and also p is positive hence it will opens to the right.
As focus is inside the parabola and it is p units to the right of the vertex:
hence
focus of parabola (h + p, k)=(-2+3/2 , 4)
=(-0.5,4)
3)
Comparing with the above standard form we get
k=4, h=-2, p=3/2
Since the given parabola is parallel to x-axis and also p is positive hence it will opens to the right.
As directrix is outside the parabola and it is p units to the left of the vertex:
hence
directrix x=h-p
= -2-3/2
=-7/2
= -3.5
y= 4
4)
Finding Axis of symmetry:
as the vertex is (-2,4) also the given parabola is parallel to x-axis so
the axis of symmetry is a horizontal straight line passing through the vertex at y=4 !