To find the x-intercepts of the quadratic function f(x) = x^2 – 4x, we need to determine the points where the function crosses the x-axis. This happens when f(x) equals zero.
We can set up the equation:
x^2 – 4x = 0
Next, we can factor the equation:
x(x – 4) = 0
From this factored form, we can see that the solutions occur when either x = 0 or x – 4 = 0. So, solving for x gives us:
- x = 0
- x = 4
This means that the x-intercepts of the function are the points (0, 0) and (4, 0). In other words, the x-intercepts are the points on the graph where the function touches or crosses the x-axis.