calculus help me

Question

Find the range of the function f(x)=x²-2x+1 if x∈[-2:3)

Answer 1

The given function is

f(x) = x² - 2x + 1

which we can rewrite as

f(x) = (x - 1)²

This equation represents a parabola that opens upwards with the vertex at (1, 0). So, the graph of f(x) covers all values of y ≥ 0. Therefore, the range is [0, ∞).

Answer 2

The above answer gives the range of the entire function how we are asked for the range in the interval from -2<x<or =3

so substitute -2 and 3 in the equation to get the y values for these x inputs

(-2)^2 -2(-2) +1= 9

(3)^2 -2(3) +1 = 9 -6 +1= 4

so range goes from 9 at x =-2 and 4 at x=3

But the vertex or minimum point is at 1,0 so range is between 0-9 with 9 excluded Graph it and you will see