SOLUTION: I really appreciate any help I can get on solving this problem: If: f(x)= 2x + 12 g (x) = 2x squared - 8x + 2 What are the points where they intersect, without graphing?

Question 333032: I really appreciate any help I can get on solving this problem:
If:
f(x)= 2x + 12
g (x) = 2x squared - 8x + 2
What are the points where they intersect, without graphing?
I tried to set them equal to each other and then solve for zero. Am I heading in the right direction?

Thank you in advance!

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If:
f(x)= 2x + 12
g (x) = 2x squared - 8x + 2
What are the points where they intersect, without graphing?
Set them equal to each other, that's where they intersect.
--------------

(The graph is not that of the original functions.)

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 : .

Discriminant d=180 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.85410196624968, -0.854101966249685. Here's your graph:

--------------------
(The graph is not that of the original functions.)
x = 5/2 � 3sqrt(5)/2
---------------
x = 5/2 + 3sqrt(5)/2
y = 17 + 3sqrt(5)
--> (5/2 + 3sqrt(5)/2,17 + 3sqrt(5))
----------------
x = 5/2 - 3sqrt(5)/2
y = 17 - 3sqrt(5)
--> (5/2 - 3sqrt(5)/2,17 - 3sqrt(5))

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