Hi

Using the vertex form of a parabola,  where(h,k) is the vertex

f(x)= 2x^2-4x+1   |putting into the vertex form by completing the square

f(x)= 2[x^2-2] +1 

f(x)= 2[(x - 1)^2 - 1] + 1 

f(x)= 2(x - 1)^2 -2 + 1 

f(x)= 2(x - 1)^2 -1 |vertex is Pt(1, -1)

f(x) is increasing from -1 to infinity 



 

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
 





The vertex is found using the formula for (x,y):



(-b/2a,f(-b/2a))



find 



...so we have (1,y)..now find 















................ so  the vertex is  (1,-1)







the intervals on which the function is increasing and the intervals on which the function is decreasing



Given the vertex of (1,-1):



The function is decreasing on:



(-∞,1)



The function is increasing  on:



(1,∞)













 

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