Mastering the Vertex Formula | How to Find the Coordinates of the Turning Point in a Quadratic Function

Vertex formula

The vertex formula is a formula used to find the coordinates of the vertex (or turning point) of a quadratic function in the form of f(x) = ax^2 + bx + c

The vertex formula is a formula used to find the coordinates of the vertex (or turning point) of a quadratic function in the form of f(x) = ax^2 + bx + c.

The coordinates (h, k) of the vertex of the quadratic function can be found using the vertex formula:

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

In this formula, “h” represents the x-coordinate of the vertex and “k” represents the y-coordinate of the vertex. “a”, “b”, and “c” are coefficients of the quadratic function.

To use the vertex formula, follow these steps:

1. Identify the values of “a”, “b”, and “c” from the quadratic function.
2. Plug these values into the vertex formula to find the x-coordinate of the vertex: h = -b / (2a).
3. Substitute the value of “h” back into the original quadratic function to find the y-coordinate of the vertex: k = f(h).

For example, let’s say we have the quadratic function f(x) = 2x^2 – 4x + 3.

1. Identify the values of “a”, “b”, and “c” as a = 2, b = -4, and c = 3.
2. Substitute these values into the vertex formula: h = -(-4) / (2 * 2) = 4 / 4 = 1.
Therefore, the x-coordinate of the vertex is 1.
3. Substitute h = 1 back into the original quadratic function to find the y-coordinate of the vertex: k = f(1) = 2(1)^2 – 4(1) + 3 = 2 – 4 + 3 = 1.
Therefore, the y-coordinate of the vertex is 1.

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

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