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

Step-by-step 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.

2

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.