How to find the vertex of a parabola?

The vertex of a parabola can be found using a simple formula. The reference shows how to find the vertex.

Vertex Formula

The key to finding the vertex of a parabola lies in the formula:

• x = -b / 2a

This formula gives you the x-coordinate of the vertex. Where a and b are coefficients from the standard form of a quadratic equation: ax² + bx + c = 0.

Steps to Find the Vertex

Here's a step-by-step guide:

1. Identify 'a' and 'b': Look at your quadratic equation in the standard form ax² + bx + c. Determine the values of a and b.

2. Apply the Formula: Plug the values of a and b into the formula x = -b / 2a. This will give you the x-coordinate of the vertex.

3. Find the y-coordinate: Substitute the x-coordinate you just found back into the original quadratic equation. Solve for y. This will give you the y-coordinate of the vertex.

4. Write the Vertex: The vertex is represented as a coordinate point (x, y).

Example

Let's say you have the quadratic equation: y = 2x² + 8x - 3

1. a = 2, b = 8

2. x = -8 / (2 * 2) = -8 / 4 = -2

3. y = 2(-2)² + 8(-2) - 3 = 2(4) - 16 - 3 = 8 - 16 - 3 = -11

4. Vertex: (-2, -11)