Question

Write in the form y−k=a(x−h)^2 or x−h=a(y−k)^2. Find the vertex, focus, and directrix. 8−2x=3(y+1)^2

Answer 1

• x -4 = (-3/2)(y +1)^2
• vertex: (4, -1)
• focus: (3 5/6, -1)
• directrix: x = 4 1/6

Explanation:

To get your desired form, you must divide the equation by -2. Then you have ...

x -4 = (-3/2)(y +1)^2

This form shows you the vertex is (h, k) = (4, -1).

When the scale factor "a" is written as 1/(4p), then the value of p is the distance from the focus to the vertex. We can find p from ...

(-3/2) = 1/(4p)

p = 1/(4(-3/2)) = -1/6

Since the parabola opens to the left, the focus is ...

(4-1/6, -1) = (3 5/6, -1)

and the directrix is in the opposite direction, at x = 4 1/6.