At how many points does the graph of the function below intersect the $x$ axis?
\[
y=25 x^{2}-10 x+1
\]
A. 1
B. 0
C. 2

Step 1 ：Given the quadratic function \(y=25x^{2}-10x+1\), we are asked to find at how many points the graph of the function intersects the x-axis.

Step 2 ：The graph of a function intersects the x-axis where the y-value is zero. So, we need to solve the equation \(25x^{2}-10x+1=0\) for x.

Step 3 ：We can solve this equation using the discriminant method. The discriminant of a quadratic equation \(ax^{2}+bx+c=0\) is given by \(b^{2}-4ac\).

Step 4 ：Substituting the coefficients a = 25, b = -10, and c = 1 into the formula, we get the discriminant as \((-10)^{2}-4*25*1=0\).

Step 5 ：The discriminant is zero, which means there is one solution to the equation. Therefore, the graph of the function intersects the x-axis at one point.

Step 6 ：Final Answer: \(\boxed{A. 1}\)