vertex
The vertex of a mathematical function is a critical point on the graph where the function reaches its highest or lowest point
The vertex of a mathematical function is a critical point on the graph where the function reaches its highest or lowest point. It is also known as the turning point of the graph.
In the case of a quadratic function written in the form of f(x) = ax^2 + bx + c, the vertex can be found using the formula x = -b/2a.
Here are the steps to find the vertex using this formula:
1. Identify the values of a, b, and c from the quadratic equation. For example, if you have the equation f(x) = 2x^2 + 4x – 1, then a = 2, b = 4, and c = -1.
2. Plug these values into the vertex formula x = -b/2a. In this case, x = -4/(2*2).
3. Simplify the formula and solve for x. In this example, x = -1.
4. To find the y-coordinate of the vertex, substitute the value of x into the original equation. So, f(-1) = 2(-1)^2 + 4(-1) – 1. Simplifying this gives f(-1) = 2 – 4 – 1 = -3.
5. Therefore, the coordinates of the vertex are (-1, -3).
It is important to note that the vertex formula described above only applies to quadratic functions. For other types of functions, different methods may be required to find the vertex.
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