which question reveals the maximum or minimum value of f(x) without changing the form of the equation?

Question

a. f(x)=(x-1)(x-1)

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

c. f(x)=(x-1)^2=2

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

Answer 1

a)

 

This function has zeros of 1.  Since this is a repeating root of a quadratic function, the graph of this function touches the x-axis at x=1.  This is where the minimum occurs.

 

 

c)

 

Your function is in vertex form.  The vertex coordinate is your minimum

 

 

d)

 

Find the zeros of the function.  Then evaluate the function at the average of the zeros.

 

 

Note:  Every question is the same written differently.

Answer 2

I think you meant "Which equation ..." rather than "Which question ...".  Any way, the answer is c) f(x) = (x-1)² - 2.  This equation is in the vertex form of a quadratic equation, y = a(x-h)² + k  where (h,k) is the location of the vertex of the parabola.  The vertex will be the minimum value of f(x) if a>0.  It will be the maximum value if a<0.