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 reflection across the x-axis translation of 2 units down translation of 1 unit left translation of 2 units up vertical stretch by a factor of 2 horizontal stretch by a factor of 2 translation of 1 unit right

Using translation concepts, it is found that these following transformations happened:

The parent function points upward and has vertex at (0,0).

A similar problem is given at link

Step-by-step explanation:

Equation of a parabola is represented by,

f(x) = -a(x - h)² + k [Parabola opening downwards]

where (h, k) is the vertex of the parabola.

Picture attached shows the vertex as (-1, -2)

Therefore, equation of the transformed parabola will be,

f(x) = -a(x + 1)²- 2

Since the given parabola passes through a point (1, -3)

-3 = -a(1 + 1)² - 2

-1 = -4a²

a =

a =

Therefore, equation of the transformed function will be,

f(x) =

If the original or parent function is g(x) = x²,

Transformed function will have the following characteristics,

1). Function will have vertex as (-1, -2) opening downwards.

2). Graph passes through (-3, -3) and (1, -3).

3). Reflection across x-axis.

4). Translation of 2 units down and 1 unit to the left.

5). Horizontal stretch by a factor of 2.