SOLUTION: 1. Graph the following quadratic functions F(x)= -x^2-2x+2 F(x)= -x^2+3x+2 F(x)= x^2+2x+2 F(x)= x^2-2x-2 2. Solve the equation and check the proposed solutions 2/x+2/x

Algebra ->  Graphs -> SOLUTION: 1. Graph the following quadratic functions F(x)= -x^2-2x+2 F(x)= -x^2+3x+2 F(x)= x^2+2x+2 F(x)= x^2-2x-2 2. Solve the equation and check the proposed solutions 2/x+2/x      Log On


   

Question 150372: 1. Graph the following quadratic functions
F(x)= -x^2-2x+2
F(x)= -x^2+3x+2
F(x)= x^2+2x+2
F(x)= x^2-2x-2


2. Solve the equation and check the proposed solutions 2/x+2/x+1 = 3x-1/x^2-1. Show all work
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. Graph the following quadratic functions
a. F(x)= -x^2-2x+2
b. F(x)= -x^2+3x+2
c. F(x)= x^2+2x+2
d. F(x)= x^2-2x-2
2. Solve the equation and check the proposed solutions 2/x+2/x+1 = 3x-1/x^2-1. Show all work
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1a F%28x%29+=+-x%5E2-2x%2B2
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B-2x%2B2+=+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=%28-2%29%5E2-4%2A-1%2A2=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+12+%29%29%2F2%5C-1+=+-2.73205080756888
x%5B2%5D+=+%28-%28-2%29-sqrt%28+12+%29%29%2F2%5C-1+=+0.732050807568877

Quadratic expression -1x%5E2%2B-2x%2B2 can be factored:
-1x%5E2%2B-2x%2B2+=+%28x--2.73205080756888%29%2A%28x-0.732050807568877%29
Again, the answer is: -2.73205080756888, 0.732050807568877. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-2%2Ax%2B2+%29

Further simplified:
x1 = -1+sqrt(3)
x2 = -1-sqrt(3)
++++++++++++++++++
The other 3 are done the same way.
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2. This is ambiguous and needs clarification.
The right side could mean 3x - (1/x^2) - 1, or 3x - 1/(x^2-1). Add parentheses, they're free.