The only two true characteristics are:
1) "The domain is all real numbers."
3) "The y-intercept is 3"
Which characteristics are true?
We have the quadratic function f(x) = (x + 1)^2 + 2 and we want to see which characteristics apply to it. Let's analyze each given option.
1) " The domain is all real numbers."
True, this is true for all quadratic functions.
2) "The range is all real numbers greater than or equal to 1."
This is an increasing quadratic function, and the minimum happens when the parentheses is equal to zero, so the minimum is y = 2, meaning that the range is all the real numbers equal or greater than 2, so this is false.
3) "The y-intercept is 3"
The y-intercept is what we get when we evaluate in x = 0, here in did, the y-intercept is at y = 3.
4) "The graph of the function is 1 unit up and 2 units to the left from the graph of y = x^2"
If we apply that translation, we get:
g(x) = (x - 2)^2 + 1
This is not our function, so this is false.
5) "The graph has two x-intercepts."
False, the minimum value of y is y = 2 (then y never becomes equal to zero), so there is no x-intercept.
Concluding, the true options are:
1) "The domain is all real numbers."
3) "The y-intercept is 3"
If you want to learn more about quadratic functions, you can read:
https://brainly.com/question/10449635
