(-b/2a, f(-b/2a))
The expression (-b/2a, f(-b/2a)) represents a point on the graph of a quadratic function
The expression (-b/2a, f(-b/2a)) represents a point on the graph of a quadratic function.
In a quadratic function of the form f(x) = ax^2 + bx + c, the graph is a parabola. The x-coordinate of the vertex of this parabola is given by -b/2a, and the y-coordinate is obtained by evaluating the function at this x-coordinate, which is f(-b/2a).
To understand this further, let’s break it down:
1. x-coordinate of the vertex: -b/2a
The formula for finding the x-coordinate of the vertex of a quadratic function is given by -b/2a. In a quadratic equation in standard form (ax^2 + bx + c = 0), a is the coefficient of x^2, and b is the coefficient of x. By substituting these values into the formula -b/2a, you can find the x-coordinate of the vertex.
2. y-coordinate of the vertex: f(-b/2a)
To find the y-coordinate of the vertex, you need to substitute the x-coordinate (-b/2a) into the quadratic function f(x). Evaluating the function f(-b/2a) will give you the corresponding y-coordinate of the vertex.
Therefore, the expression (-b/2a, f(-b/2a)) represents the coordinates (x, y) of the vertex of a quadratic function.
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