f(x) = -3x^2 + 6x

Question

maximun/minimum

Answer 1

Without calculus you have to memorize that extrema (min or max) happen at x=-b/(2a)

 

for the quadraric 

f(x)=ax² + bx + c

 

for your equation

x=-6/(-6)=1

 

The zeros of your equation are 0, 2. The extrema is in the middle of the zeros. 

 

Since for your equation a is negative your parabola goes down. It is like an upside down U. Therefore the extrema is a maximum. The functional value at f(1)=3. 

Answer 2

f(x)=-3x²+6x=-3(x²-2x)=-3((x-1)²-1)=-3(x-1)²+3

vertex is at (1,3) it is a max since parabola is opening downward.