SOLUTION: I have to write each function in vertex form, and identity it's vertex. g(x)=x^2-1/2x+1 could you please guide me on the step by step process on how to work this. please h

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I have to write each function in vertex form, and identity it's vertex. g(x)=x^2-1/2x+1 could you please guide me on the step by step process on how to work this. please h      Log On


   

Question 162179: I have to write each function in vertex form, and identity it's vertex.
g(x)=x^2-1/2x+1
could you please guide me on the step by step process on how to work this.
please help soon!
thx :)
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-%281%2F2%29x%2B1 Start with the given expression.


Take half of the x coefficient -1%2F2 to get -1%2F4. In other words, %281%2F2%29%28-1%2F2%29=-1%2F4.


Now square -1%2F4 to get 1%2F16. In other words, %28-1%2F4%29%5E2=%28-1%2F4%29%28-1%2F4%29=1%2F16


x%5E2-%281%2F2%29x%2Bhighlight%281%2F16-1%2F16%29%2B1 Now add and subtract 1%2F16. Make sure to place this after the "x" term. Notice how 1%2F16-1%2F16=0. So the expression is not changed.


%28x%5E2-%281%2F2%29x%2B1%2F16%29-1%2F16%2B1 Group the first three terms.


%28x-1%2F4%29%5E2-1%2F16%2B1 Factor x%5E2-%281%2F2%29x%2B1%2F16 to get %28x-+1%2F4%29%5E2.


%28x-1%2F4%29%5E2%2B15%2F16 Combine like terms.


So after completing the square, x%5E2-%281%2F2%29x%2B1 transforms to %28x-1%2F4%29%5E2%2B15%2F16. So x%5E2-1%2F2x%2B1=%28x-1%2F4%29%5E2%2B15%2F16.


So g%28x%29=x%5E2-%281%2F2%29x+%2B1 is equivalent to g%28x%29=%28x-1%2F4%29%5E2%2B15%2F16.


Notice how g%28x%29=%28x-1%2F4%29%5E2%2B15%2F16 is in vertex form y=a%28x-h%29%5E2%2Bk where the vertex is (h,k)


Since h=1%2F4 and k=15%2F16, this means that the vertex is

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Write in vertex form: a%28x-h%29%5E2%2Bk+=+0:
You can convert to the vertex form of the equation by "completing the square"
g%28x%29+=+x%5E2-%281%2F2%29x%2B1 Set this function equal to zero.
x%5E2-%281%2F2%29x%2B1+=+0 Subtract 1 from both sides.
x%5E2-%281%2F2%29x+=+-1 Add the square of half the x-coefficient to both sides, that's %28-1%2F4%29%5E2+=+1%2F16)
%28x%5E2-%281%2F2%29x%2B+1%2F16%29+=+1%2F16-1 Factor the trinomial on the left side.
%28x-1%2F4%29%5E2+=+-15%2F16 Add 15%2F16 to both sides.
%28x-1%2F4%29%5E2%2B15%2F16+=+0 Compare with the standard vertex form:
a%28x-h%29%5E2%2Bk+=+0 The vertex is located at (h, k), so,h+=+1%2F4 and k+=+15%2F16
The vertex in your equation is located at: (1%2F4,15%2F16)
Check the graph of the equation:
graph%28400%2C400%2C-2%2C2%2C-2%2C2%2Cx%5E2-%281%2F2%29x%2B1%29