Select all the transformations of f(x) = x2 that combine to result in the graph of function g below. A parabola with vertex negative 1 comma negative 2 that opens downward. The graph passes through the points negative 3 comma negative 3 and 1 comma negative 3.

Group of answer choices

vertical stretch by a factor of 2

translation of 1 unit right

translation of 2 units up

translation of 1 unit left

reflection across the x-axis

horizontal stretch by a factor of 2

translation of 2 units down

Options 4, 5 and 7.

Step-by-step explanation:

The general function is

The vertex form of a parabola,

       ...(1)

where, a is a constant and (h,k) is vertex.

It is given that vertex of a parabola is (-1,-2).

      ...(2)

It passes through (-3,-3).

Put this value in (2).

Now,

h=1>0, so translation of 1 unit left.

a=-1/4<0 Reflection across the x-axis and vertical compression by factor 4.

k=-2<0, translation of 2 units down

Therefore, the correct options are 4, 5 and 7.

answerthe vertex form

step-by-step explanation: