Math homework question?

Question

Find the minimum or maximum value of the quadratic function
f(x)=x^2-6x+4

Answer 1

min value
the turning point is min point.

r=-b/2a =3
k=(4ac-b^2)/4a=-20/4=-5


a=1
b=-6
c=4


min value (put x=3 in the function)
f(3)=9-18+4
= - 5

Answer 2

You have to find f'(x), since this gives the slope of the line. Where the slope of the line = 0, that gives the max or the min. It's a max if f(x) points down (the coefficient o x^2 is < 0) and min if f(x) points up.
In this case, f'(x) is 2x - 6. This equals zero only when x = 3. We know it's a minimum because f(x) points up.
Plug x back in to f(x) to find that f(3) = -3

Answer 3

I would approach this by finding the derivative, and then solving for any points where the derivative is zero. You can use the second derivative to determine if the point is a max or min.

Answer 4

http://www.coolmath.com/graphit/index.html

this website has an online graphing calculator - put in your equation to see the graph and the minimum value of the function.