Answer:
[1,∞)
Explanation:
Let's try to plug in some numbers.
When solving a problem fo range, the best place to start is where you can let the (x - b) part = 0.
This is what I mean
3(x-6)² + 1
Let x = 6
3(0)² + 1 = 1
Look how we have a 0 inside the parentheses.
That's what I mean.
Now let's try using terms smaller than 6.
Now, let's try plugging in 5
3(-1)² + 1 = 4
Now try plugging in 4
3(-2)² + 1 = 13
Looks like we will just keep going up.
Now let's try using terms bigger than 6.
Plugging in 7
3(1)² + 1 = 4
Plugging in 8
3(2)² + 1 = 13
We just go up both ways because of the x squared term.
So our smallest value is at x = 6 where we have y = 1.
If we go either direction forever to the right or left the terms to get bigger, where it approaches infinity.
So, 1 will have parentheses as it can be reached and infinity will have parentheses as it is unreachable and goes on forever.
[1,∞)