SOLUTION: for given function f (x) = 1-xsquared.

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Question 171446: for given function f (x) = 1-xsquared.
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B0x%2B1+=+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%2A-1%2A1=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+4+%29%29%2F2%5C-1+=+-1
x%5B2%5D+=+%28-%280%29-sqrt%28+4+%29%29%2F2%5C-1+=+1

Quadratic expression -1x%5E2%2B0x%2B1 can be factored:
-1x%5E2%2B0x%2B1+=+-1%28x--1%29%2A%28x-1%29
Again, the answer is: -1, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B0%2Ax%2B1+%29