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

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.

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