Understanding the Vertex: Definition, Properties, and How to Find the Vertex of a Quadratic Function

vertex

In mathematics, the vertex refers to a point where two or more lines, edges, or curves meet

In mathematics, the vertex refers to a point where two or more lines, edges, or curves meet. It is commonly represented as a dot or a point in a graph or a drawing.

In geometry, the vertex is often used to describe the point where two or more sides of a polygon intersect. For example, in a triangle, each of the three corners is considered a vertex. In a rectangle, all four corners are referred to as vertices.

In algebra, the vertex is frequently used to describe the maximum or minimum point of a parabola. A parabola is a U-shaped curve that can open upwards or downwards. The vertex is the point where the curve changes direction and is often denoted as (h, k). If the parabola opens upwards, the vertex represents the minimum point of the curve. Conversely, if the parabola opens downwards, the vertex represents the maximum point.

To find the vertex of a quadratic function in the form of y = ax^2 + bx + c, you can use the following formula:

h = -b / (2a)
k = f(h)

Here, h represents the x-coordinate of the vertex, and k represents the y-coordinate. The values of a, b, and c are coefficients of the quadratic equation.

For example, let’s consider the quadratic function y = 2x^2 – 4x + 3. To find the vertex:

Step 1: Identify the coefficients: a = 2, b = -4, c = 3.
Step 2: Use the formula to find h: h = -(-4) / (2 * 2) = 4 / 4 = 1.
Step 3: Substitute h into the original equation to find k: k = 2(1)^2 – 4(1) + 3 = 2 – 4 + 3 = 1.
Step 4: The vertex is given by (h, k), so the vertex in this case is (1, 1).

Therefore, the vertex of the quadratic function y = 2x^2 – 4x + 3 is (1, 1).

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