SOLUTION: Where do the two graphs {{{f(x)=x^2+2}}} and {{{g(x)=x-8}}} intersect?

Question 438459: Where do the two graphs and intersect?
Found 3 solutions by Gogonati, Alan3354, josmiceli:
Answer by Gogonati(855)   (Show Source): You can put this solution on YOUR website!
To find the intersection points we solve the equation: or
, since D<0, this equation has not real root, therefore these two
graphs not intersected.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Where f(x) and g(x) are equal.

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -39 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 -39 is + or - .

The solution is , or
Here's your graph:

---------
The solutions are not real numbers, so the graphs do not intersect.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
They intersect where

There can be no intersection, because there is no way
the left side can equal the right
can only be positive
-------------------
Here's the graph:

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