Question

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

Answer 1

To move the vertex of the quadratic function from the point \((-3, -2)\) to the point \((0, 0)\), we need to determine the transformations required.

1. **Identify the differences in the x-coordinates:**
- The current x-coordinate is \(-3\) and we want to move to \(0\).
- The transformation requires moving from \(-3\) to \(0\). This is a shift to the **right** by \(3\) units.

2. **Identify the differences in the y-coordinates:**
- The current y-coordinate is \(-2\) and we want to move to \(0\).
- The transformation requires moving from \(-2\) to \(0\). This is a shift **up** by \(2\) units.

Putting it all together, to translate the vertex from \((-3, -2)\) to \((0, 0)\), you must shift **right 3 units and up 2 units**.

Thus, the correct transformation is:

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