Final answer:
The vertex of the function f(x) = x^2 - 4x is (2, -4), and the x-intercepts are 0 and 4.
Step-by-step explanation:
The given function is of the form f(x) = ax^2 + bx + c, where a = 1, b = -4, and c = 0. To find the vertex of the function, we can use the formula x = -b/2a. Plugging in the values, we get x = -(-4)/2(1) = 2. Therefore, the x-coordinate of the vertex is 2. To find the y-coordinate, we substitute the x-coordinate into the function: f(2) = (2)^2 - 4(2) = -4. Thus, the vertex of the function f(x) = x^2 - 4x is (2, -4).
To find the x-intercepts of the function, we set f(x) = 0 and solve for x. So, x^2 - 4x = 0 → x(x - 4) = 0. This equation is satisfied when x = 0 or x - 4 = 0. Therefore, the x-intercepts of the function are x = 0 and x = 4.
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