A quadratic function on a graph has the vertex at the point (−3,−2). Which of the following transformations translates the vertex to the point (0,0)

Question

Responses

shift left 2 units and down 3 units

shift right 3 units and down 2 units

shift left 3 units and up 2 units

shift right 3 units and up 2 units

Answer 1

To determine the transformation needed to translate the vertex of a quadratic function from the point (-3, -2) to (0, 0), we can analyze the changes in the x and y coordinates.

1. Change in x-coordinates:

   • From -3 to 0, the x-coordinate increases by 3 units (0 - (-3) = 3). This means we need to shift right 3 units.

2. Change in y-coordinates:

   • From -2 to 0, the y-coordinate increases by 2 units (0 - (-2) = 2). This means we need to shift up 2 units.

Combining both transformations, we conclude that the correct transformation is to shift right 3 units and up 2 units.

Therefore, the correct response is:

shift right 3 units and up 2 units.