Does the function #f(x)= -x^2+6x-1# have a minimum or maximum value?

1 Answer
Jan 28, 2017

Answer:

The parabola will have a maximum value because the #x^2# term is negative.

Explanation:

  1. Because the function has the general form #f(x)=color(blue)(A)x^2+color(purple)(B)x+color(red)(C)#, we know the graph will be a parabola.
  2. The sign of the #x^2# term will tell us if the parabola opens up (like a #uu#) or down (like a #nn#):

If #A >0#, opens up (#uu#)

If #A<0#, opens down (#nn#)

In this case,
#f(x)=color(blue)(-(1))x^2color(purple)(+6)xcolor(red)(-1)#
#color(blue)(A = -1)# so the parabola will open "down" or #nn# which means the parabola will have a "peak" or maximum point.

graph{-x^2+6x-1 [-15, 15, -10, 10]}