Question

Find the vertex of this parabola: -x^2+6x-8

Answer 1

f '(x)=-2x+6
f '(x)=0 --> 2x=6
x=3
y=f(3)=1

Answer 2

are you really supposed to use calculus for this? if not your teacher will think either you lost your mind or you cheated

Answer 3

if you are not taking calculus you might want to write
\[-\frac{b}{2a}=-\frac{6}{2\times -1}=3\] and then use
\[-3^2+6\times 3-8=-9+18-8=1\] to get the vertex is
\[(3,1)\]

Answer 4

It's the same method, except you're not thinking and just filling out formulas.

Answer 5

like hell it is

Answer 6

you do not need calculus to find the vertex of a quadratic. all you need is common sense. you write it in the form
\[a(x+\frac{b}{2a})^2+k\] and make the rather trivial observation that this has a max or min when
\[x=\frac{-b}{2a}\] and when it does you get k. finito

Answer 7

'not thinking' is "take the derivative, set it equal zero and solve" as if i need to take a limit to do this easy problem

Answer 8

Fair enough, I didn't think of that way to get -b/2a, because you also get -b/2a with the derivative. Still either way is easy.

Answer 9

but of course you are right, either way you get it. ;)