Question

what is the power function end behavior model of
f(x)= 3x^2-2x+1 and how do you find it?

Answer 1

This is a quadratic function, a parabola
It has complex zeros (1/3)(1 +/- i sqrt 2) so does not cross the x axis.
What happens as x goes to +oo or - oo?
as |x| gets big, x^2 is >> x or 1 so it acts like y = 3 x^2 for large plus or minus x
So it is an upright parabola (holds water)
Let's find the vertex
3 x^2 - 2x = y-1
x^2 - 2/3 x = y/3 - 1/3
x^2 - 2/3 x + 1/9 = y/3 -2/9
(x-1/3)^2 = (1/3)(y-2/3)
vertex at (1/3, 2/3)