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 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
shift right 3 units and down 2 units

shift left 3 units and up 2 units

Answer 1

To find the correct transformation that translates the vertex of the quadratic function from \((-3, -2)\) to \((0, 0)\), we need to determine the changes needed in both the x-coordinate and y-coordinate.

1. **Current vertex:** \((-3, -2)\)
2. **Target vertex:** \((0, 0)\)

**Changes in Coordinates:**
- From \(-3\) to \(0\): This is a shift to the right by \(3\) units (since \(0 - (-3) = 3\)).
- From \(-2\) to \(0\): This is a shift upward by \(2\) units (since \(0 - (-2) = 2\)).

Therefore, the necessary transformation is to **shift right 3 units and up 2 units**.

**Correct response:** shift right 3 units and up 2 units.