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 3 units and up 2 units
shift left 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 appropriate transformation that moves the vertex of the quadratic function from \((-3, -2)\) to \((0, 0)\), we need to calculate the shift in both the x-coordinate and the y-coordinate.

1. **X-coordinate**:
- Current x-coordinate = \(-3\)
- Target x-coordinate = \(0\)
- Shift = \(0 - (-3) = 3\) units to the right.

2. **Y-coordinate**:
- Current y-coordinate = \(-2\)
- Target y-coordinate = \(0\)
- Shift = \(0 - (-2) = 2\) units up.

Thus, to move the vertex from \((-3, -2)\) to \((0, 0)\), we need to **shift right 3 units** and **up 2 units**.

So, the correct transformation is:

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