Question

find the coordinates for the vertex of the following quadratic function. show your work here

Explanation:

Step1: Identify vertex definition

The vertex of a parabola (quadratic function graph) is its minimum (for upward - opening) or maximum (for downward - opening) point. Here, the parabola opens upward, so we look for the lowest point.

Step2: Locate x - coordinate

On the graph, we check the horizontal (x - axis) position of the vertex. By looking at the grid, the vertex is at \(x = 3\) (since it's 3 units to the right of the origin on the x - axis).

Step3: Locate y - coordinate

Now, check the vertical (y - axis) position. The vertex is at \(y=2\) (2 units above the origin on the y - axis).

Answer:

The coordinates of the vertex are \((3, 2)\)