Range of these quadratic functions?

Question

I know that the domain is positive infinity to negative infinity.
However, what is the range of these quadratic functions?
y=x^2
y=(x+3)^2-4
y=-(x-2)^2-1
*Please write in interval notation.

Answer 1

y=x^2 range would be all positive real numbers because the parabolas vertex is (0,0) and it is facing up.

y=(x+3)^2-4 takes the parabola above and moves it left 3 spaces and down 4 spaces so the vertex is (-3,-4) meaning the range is from -4 to positive infinity.

y=(x-2)^2-1 takes the first parabola and moves it 2 spaces to the right and 1 space down so the vertex is(2,-1) meaning the range if from-1 to positive infinity.

Answer 2

know that the domain is positive infinity to negative infinity.

However, what is the range of these quadratic functions?



y=x^2

range is 0 to +infinity



y=(x+3)^2-4

range is -4 to + infinity



y=-(x-2)^2-1

range is -1 to - infinity





I think this is correct

Answer 3

1. all non negative numbers.

2. all numbers equal to or greater than -4

3. all numbers less than or equal to -1

Answer 4

First one [0,inf)



the rest are as easy as that arent they?