This is a quadratic function. The graph of a quadratic function is a parabola.

To find the x-intercepts, we set f(x) = 0 and solve the equation:
3x^2 - 24x + 1 = 0

We can use the quadratic formula to solve for x:
x = (-(-24) ± sqrt((-24)^2 - 431))/(2*3)
x = (24 ± sqrt(576 - 12))/6
x = (24 ± sqrt(564))/6
x = (24 ± 23.77)/6
x = 7.79 or x = 3.87

So the x-intercepts are approximately x = 7.79 and x = 3.87.

To find the y-intercept, we set x = 0 and evaluate f(x):
f(0) = 3(0)^2 - 24(0) + 1
f(0) = 0 - 0 + 1
f(0) = 1

So the y-intercept is at approximately y = 1.

The graph of the function f(x) = 3x^2 - 24x + 1 will be a parabola opening upwards, with x-intercepts at approximately x = 7.79 and x = 3.87, and a y-intercept at y = 1.