# Which equation represents a graph with a vertex at (-3, 2)?

Updated on January 19, 2024

Answer: The equation that represents a graph with a vertex at (-3, 2) is y = 4x² + 24x + 38.

## Vertex Form of a Quadratic Function

The vertex form of a quadratic function is y = a(x – h)² + k, where (h, k) is the vertex. To determine which equation represents a graph with a vertex at (-3, 2), look for an equation that, when completed the square, gives the vertex form with h = -3 and k = 2. The equation y = 4x² + 24x + 38 can be rewritten in vertex form to represent this vertex. Understanding this concept is fundamental in algebra and geometry for analyzing quadratic functions and their graphs.

## FAQ on Vertex Form of a Quadratic Function

### How do you find the vertex of a quadratic function?

Use the formula h = -b/2a for standard form or identify (h, k) in vertex form.

### How do you convert standard form to vertex form?

Complete the square and rewrite the equation in vertex form.

### Why is the vertex form useful?

It provides a direct way to identify the vertex and the direction of the parabola.