Question

Find the domain and range of the function
f(x)=x^2-12x+2

Answer 1

y = f(x) = x^2-12x +2
Let's complete the square to see what this parabola looks like
x^2-12 x = y-2
x^2-12 x +36 = y+34
(x-6)^2 = y+34
Well, this parabola is symmetric about the vertical line where x = 6
As x gets big positive or negative, y gets big so this parabola is upright, holds water.
So the domain of y is all real x.
The left side is always positive, so y+34 never gets less than zero, so y never gets less than -34
so the range of y is all real y greater than or equal to -34

Answer 2

Typo - I mean the domain of x is all real x

Answer 3

thanks