SOLUTION: Can you help me: find the vertex, value of p, axis of symmetry, focus, and Directrix of each parabola? 1. y=1/8(x-1)^2 2. x=2y^2 +1 3. x-2=1/2(y+1)^2

Question 927264: Can you help me: find the vertex, value of p, axis of symmetry, focus, and Directrix of each parabola?
1. y=1/8(x-1)^2
2. x=2y^2 +1
3. x-2=1/2(y+1)^2
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
the vertex form of a Parabola opening up(a>0) or down(a<0),

where(h,k) is the vertex and x = h is the Line of Symmetry ,
the focus is (h,k + p), With Directrix y = (k - p), a = 1/(4p)
............

y=1/8(x-1)^2 Parabola Opening Upward a = 1/8 > 0
vertex, (1,0)
value of p, a = 1/8 = 1/(4p), p = 2
axis of symmetry, x = 1
focus (1, 2)
Directrix: y = -2
...........
the vertex form of a Parabola opening right(a>0) or left(a<0),

where(h,k) is the vertex and y = k is the Line of Symmetry,
the focus is (h +p,k ), With Directrix x = (h - p) , a = 1/(4p)
..........
2. x=2y^2 +1
vertex, (1,0)
value of p, a = 2 = 1/(4p), p = 1/8
axis of symmetry, y = 0
focus (9/8, 0)
Directrix: x = 7/8
.......
3. x=1/2(y+1)^2 + 2
vertex, (2,-1)
value of p, a = 1/2 = 1/(4p), p = 1/2
axis of symmetry, y = -1
focus (2.5, -1)
Directrix: x = 1.5

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