SOLUTION: Consider the function: f(x)=x^2+4 Will f(x) +4 have real zeros? Justify without any calculations. Will f(x) -5 have real zeros? Justify without any calculations. Will f(x-

Question 1020031: Consider the function:
f(x)=x^2+4
Will f(x) +4 have real zeros? Justify without any calculations.
Will f(x) -5 have real zeros? Justify without any calculations.
Will f(x-2) have real zeros? Justify without any calculations.
Will f(x+4) have real zeros? Justify without any calculations.
i can it with calculations but i do not have idea how to do without calculation. I would love any help.
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

Consider the function  f(x)=x^2+4
1. Will f(x) +4 have real zeros? Justify without any calculations. - No.  is just non-negative, and  has the minimum in 4 units over the zero.

2. Will f(x) -5 have real zeros? Justify without any calculations. - Yes. Its minimum is negative.

3. Will f(x-2) have real zeros? Justify without any calculations. - No. The same reason as in n.1.  Notice that f(x-2) = .

4. Will f(x+4) have real zeros? Justify without any calculations. - No. The same reason as in n.1.  Notice that f(x+4) = .

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