Determine without graphing whether the given quadratic function has a maximum value or a minimum value and then find the value f(x)=-3x^2+12x-3

Question

phi · Answer

the trick to this one is the sign of the coefficient on the x^2 term

if it is negative, then for "big x"  you will get a negative number
the graph looks like a "frown"

if the number is positive, you get a "smile"

hopefully you know which has a max and which has a min value

anonymous · Answer

yes, but whats next? okay I know its maximum, I guess I'm trying to figure out how they got 9

phi · Answer

the "vertex" of a parabola 
occurs  at  x= -b/2a     where a,b,c are the numbers:  ax^2 + bx + c
in your case,  a= -3  and b is +12   (c is -3 but we don't care for this problem)

x= -b/(2a)  means replace b with 12  and a with -3 to get

x= - 12/(2*-3) =  -12/-6  = +2

the y value is  found by replacing x with 2 in the equation

phi · Answer

see http://hotmath.com/hotmath_help/topics/vertex-of-a-parabola.html

anonymous · Answer

okay thanks, I understand now, once again Thanks!!!

phi · Answer

you can take a look at http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/solving_graphing_quadratics/v/quadratic-functions-3 as a quick refresher. He explains this stuff pretty well.