Question

find the fixed point of the function f(x)=x^2-4x+6

Answer 1

??? you mean the vertex?

Answer 2

no it is when f(c)=c

Answer 3

It just says the fixed point or points oif the function. I think that is why I am confused

Answer 4

subtract an x and quad formula then if thats the case ;)

Answer 5

This can be handled easily with the quadratic equation it would seem.

Answer 6

ok

Answer 7

I.e., as TT points out, what are the numbers c, if any such that
f(c) = c

Solve that equation.

Answer 8

where are you getting the f(c)=c

Answer 9

This is the definition of a fixed point.

Answer 10

oh they didn't tell me that. That would have been nice for my instructor to tell me that. Just starting to learn this concept.

Answer 11

Call it c, p, x, whatever you like. A number c in the domain of a function f is called a FIXED POINT of f if it has the property that f(c) = c.

Answer 12

The intuition for the name is clear: the function f leaves fixed points where they are; they are not transformed to other values.

Answer 13

ok

Answer 14

can you walk me through this

Answer 15

Does fixed point mean:
x^2-4x+6 = x

Answer 16

That is what I was going to ask

Answer 17

Geometrically, this is where the graph of f intersects the straight line y = x.

So by definition, a fixed point satisfies the equation f(c) = c. That is

c^2-4c+6 = c

Now determine what values, if any, of c satisfy that equation.

Answer 18

x^2-4x+6 = x
x^2 - 5x + 6 = 0

Answer 19

right

Answer 20

Then solve for x

Answer 21

(x-2)(x-3) = x^2 - 5x + 6
x = 2
x = 3

You get points
(2,2)
(3,3)

Answer 22

here it is geometrically,

Answer 23

thanks once I seen it draw out that seems to help.