Question

If y=x²-6x+9, Find the range of value of x for which y ≥ 0.




Pls I need working answer

Answer 1

We need all values of x for which y is positive or zero.

So, x²-6x+9 is either positive or zero.

x²-6x+9 ≥ 0
x²-6x ≥ -9
(x - 3)^2 - 9 ≥ -9
(x - 3)^2 ≥ 0
x - 3 ≥ 0
x ≥ 3

Answer 2

(x - 3)^2 ≥ 0 for all x, since it is a squared value.
The graph is a parabola just touching the x-axis at x=3.