To find the vertex of the quadratic function f(x) = x^2 – 6x, we can use the vertex formula. The standard form of a quadratic function is given by f(x) = ax^2 + bx + c, where a, b, and c are constants. In this case, we have:
- a = 1
- b = -6
- c = 0
The vertex of a parabola represented by a quadratic function can be found using the formula:
x = -b / (2a)
Substituting the values of a and b, we get:
x = -(-6) / (2 * 1) = 6 / 2 = 3
Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting x back into the original function:
f(3) = (3)^2 – 6(3) = 9 – 18 = -9
Thus, the vertex of the quadratic function f(x) = x^2 – 6x is (3, -9). This means the graph of the function reaches its minimum point at this coordinate.