SOLUTION: Hi! The question for this is: for the function f(x)= x^2 -2x+1 a)find f(0) b) solve f(x)=0 Please and Thank You=)

Algebra ->  Functions -> SOLUTION: Hi! The question for this is: for the function f(x)= x^2 -2x+1 a)find f(0) b) solve f(x)=0 Please and Thank You=)      Log On


   

Question 130389This question is from textbook algebra
: Hi!
The question for this is: for the function f(x)= x^2 -2x+1
a)find f(0)
b) solve f(x)=0

Please and Thank You=) This question is from textbook algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)
f%28x%29=x%5E2-2x%2B1 Start with the given function


f%280%29=%280%29%5E2-2%280%29%2B1 Plug in x=0


f%280%29=0-2%2A0%2B1 Raise 0 to the 2nd power to get 0


f%280%29=0-0%2B1 Multiply 2 and 0 to get 0


f%280%29=0%2B1 Subtract 0 from 0 to get 0


f%280%29=1 Add 0 and 1 to get 1



b)


f%28x%29=x%5E2-2x%2B1 Start with the given function


0=x%5E2-2x%2B1 Plug in f%28x%29=0
0=%28x-1%29%28x-1%29 Factor the right side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-1=0 or x-1=0

x=1 or x=1 Now solve for x in each case


Since we have a repeating answer, our only answer is x=1

Notice if we graph y=x%5E2-2x%2B1 we can see that the only root is x=1. So this visually verifies our answer.


+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E2-2x%2B1%29+