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?

Algebra ->  Functions -> 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?       Log On


   

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) About Me  (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.
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2x%5E2+-+8x+%2B+2+=+2x+%2B+12
2x%5E2+-+10x+-+10+=+0
(The graph is not that of the original functions.)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-10x%2B-10+=+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=%28-10%29%5E2-4%2A2%2A-10=180.

Discriminant d=180 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+180+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+180+%29%29%2F2%5C2+=+5.85410196624968
x%5B2%5D+=+%28-%28-10%29-sqrt%28+180+%29%29%2F2%5C2+=+-0.854101966249685

Quadratic expression 2x%5E2%2B-10x%2B-10 can be factored:
2x%5E2%2B-10x%2B-10+=+%28x-5.85410196624968%29%2A%28x--0.854101966249685%29
Again, the answer is: 5.85410196624968, -0.854101966249685. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-10%2Ax%2B-10+%29

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