SOLUTION: can you show me how to solve f(x)= x^2 +4 If I can see the example to find domain...I think I can explain to my son. I understand what domain is just not how to set up the proble

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Question 157185This question is from textbook
: can you show me how to solve f(x)= x^2 +4
If I can see the example to find domain...I think I can explain to my son. I understand what domain is just not how to set up the problem and work it.
 This question is from textbook

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
can you show me how to solve f(x)= x^2 +4
If I can see the example to find domain...I think I can explain to my son. I understand what domain is just not how to set up the problem and work it.
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Set f(x) = 0
x^2+4 = 0
x^2 = -4
x = +2i
x = -2i
i = sqrt(-1)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A4=-16.

The discriminant -16 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -16 is + or - sqrt%28+16%29+=+4.

The solution is x%5B12%5D+=+%28-0%2B-i%2Asqrt%28+-16+%29%29%2F2%5C1+=++%28-0%2B-i%2A4%29%2F2%5C1+, or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B4+%29