Final answer:
The value of the discriminant of f(x) is 0, indicating that the graph has one x-intercept.
Step-by-step explanation:
The discriminant of a quadratic function is the expression found under the square root of the quadratic formula. It helps determine the number of x-intercepts a function has.
The discriminant, denoted as ∆, is given by the equation: ∆ = b² - 4ac. In the given quadratic function, f(x) = 25x² - 10x + 1, the coefficients are a = 25, b = -10, and c = 1.
Plugging these values into the discriminant formula, we get: ∆ = (-10)² - 4(25)(1) = 100 - 100 = 0.
Therefore, the value of the discriminant of f is 0.
To determine the number of x-intercepts the graph of f has, we need to consider the value of the discriminant.
If the discriminant is positive, the graph will have two x-intercepts. If the discriminant is zero, the graph will have one x-intercept. And if the discriminant is negative, the graph will have no real x-intercepts.
In this case, the discriminant is 0, so the graph of f(x) = 25x² - 10x + 1 has one x-intercept.