Question

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)
? (1 point)
Responses

shift left 3 units and up 2 units
shift left 3 units and up 2 units

shift right 3 units and up 2 units
shift right 3 units and up 2 units

shift left 2 units and down 3 units
shift left 2 units and down 3 units

shift right 3 units and down 2 units

Answer 1

To determine the transformation that translates the vertex of the quadratic function from \((-3, -2)\) to \((0, 0)\), we need to analyze the movements on the coordinate plane.

1. **From (-3, -2) to (0, 0)**:
- The x-coordinate changes from \(-3\) to \(0\). This is a movement to the **right** by \(3\) units (\(0 - (-3) = 3\)).
- The y-coordinate changes from \(-2\) to \(0\). This is a movement **up** by \(2\) units (\(0 - (-2) = 2\)).

Based on this analysis, the correct transformation that translates the vertex from \((-3, -2)\) to \((0, 0)\) is:

**Shift right 3 units and up 2 units.**